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Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises

Published Online: 15 Jul 2022
Volume & Issue: AHEAD OF PRINT
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Received: 26 Apr 2022
Accepted: 23 Jun 2022
Journal Details
License
Format
Journal
eISSN
2444-8656
First Published
01 Jan 2016
Publication timeframe
2 times per year
Languages
English
Introduction

At present, many companies have recognized the importance of tax issues, and a few have recognized the existence of tax risks, and have tried their best to reduce their tax risks by improving the financial staff's business quality and employing tax consultants. The famous “Hain's Law” states: There are signs behind the accident, and there are signs behind the signs.

It is precisely because companies do not pay much attention to tax risks that have caused serious consequences. The early warning of tax risks is to find potential tax risks of the enterprise by judging the signs and signs before the occurrence of tax risks, and ask the enterprise management authorities to take corresponding measures to prevent problems before they occur [1].

According to PwC survey data, China is the country with the biggest tax challenges in Asia. In addition to traditional financial risks and operational risks, each enterprise faces different levels of tax risks. Due to the complexity of China's tax law, the tax risks of enterprises have been increased, which has proposed for the construction of tax risk research and early warning mechanisms. For urgent needs. The research on tax risks can be viewed from the perspective of tax authorities or from the perspective of enterprises. This article is from the perspective of the enterprise, analyses the possible tax risks of the enterprise, and uses relevant indicators and models to establish a scientific and effective early warning mechanism for tax risks [2].

This paper uses a combination of quantitative analysis and qualitative analysis. On the one hand, it analyses various tax risks and sizes of enterprises from a qualitative perspective; on the other hand, it uses a quantitative value to measure tax risks, and establishes a tax risk early warning mechanism through early warning indicators. In the specific analysis, the marginal analysis of classical economics is used to illustrate the principle of achieving the goal of the early warning mechanism. The method of geometric figures is used to discuss the impact of risk appetite on the early warning mechanism of tax risk. The form of scoring is used to directly display the operation of early warning of tax risk. Process [3]. The original meaning is to recognize the logical sequence of things as the basic structure. Based on the definition of legal risk and early warning, the mechanism analysis of the tax risk early warning mechanism was carried out based on this. Under the condition that the preparatory work was completed, the core part of this article introduced the tax risk early warning indicators and established the corresponding Tax risk early warning mechanism. Finally, the article verifies the construction of the tax risk early warning mechanism with a specific case, and concludes the full text with this.

Tax risk warning overview
The concept of tax risk and early warning

Tax risk belongs to the category of risk. Before understanding tax risk, it is necessary to clarify what is risk. In 1895, the American scholar Hayes gave a definition of risk from the perspective of economics. He believed that risk is “the possibility of loss”; uncertainty of probability random events is risk. Risks will only occur when there are two or more possibilities for an activity, and the occurrence of risks usually brings some form of loss. Therefore, tax risk is an uncertainty faced by enterprises in all tax-related activities, such as enterprises being inspected by tax authorities, bearing excessive tax liabilities, or incurring liabilities for tax reimbursement and fines. For the production and operation of an enterprise, the pursuit of profit is an eternal theme, but the profit of the enterprise must be controlled within an acceptable risk range. If the profit has a high risk, the enterprise will have the hidden danger of failure [4].

Tax risk has tax uncertainty. Uncertainty is the basis for tax risks. Without uncertainty, risks will not arise, and tax risks will be even more difficult to talk about. In the process of production and operation, enterprises are faced with a variety of decisions. Each decision is the result of a cost-benefit balance. The tax liability is the embodiment of each decision in tax law. Different decisions cause different tax burdens, and even the same decision will have different tax burdens due to different subjective reasons of the taxpayer and objective reasons of the external environment [5]. It should be noted that less tax and delayed taxation have tax risks, and more taxation and early taxation also have tax risks. Less tax payment and delayed tax payment means that failure to pay taxes on time and amount will be punished by tax authorities for late fees and fines, resulting in outflow of economic benefits and reduction of corporate value. By the same token, multiple taxation and early taxation will directly lead to the outflow of economic benefits and time value, reduce corporate value, and cause tax risks.

Stages and characteristics of tax risks

The generation of corporate tax risks is not caused overnight, but is a process of long-term accumulation and gradual development. In the entire development process of corporate tax risks, although these risks will show different tax characteristics, this performance may not be very significant and clear, and some may even be potential, but once it develops rapidly, it will It may enter a complete tax risk state immediately, leading to serious consequences, so the tax risk early warning requires research on the tax-related characteristics exhibited by the enterprise at different stages [6].

The formation of corporate tax risks should be divided into the following four main stages, and exhibit different characteristics. That is: tax risk incubation stage, tax risk development stage, tax risk deterioration stage and tax risk explosion stage. The different characteristics of these four stages can be described with the following figure.

In college physical education, martial arts have attracted more and more college students because of its unique charm and exercise value. In martial arts, it is easy to cause ligament damage and meniscus injury and aging. After severe meniscus injury or aging degeneration, a total meniscectomy is required. In order to prevent the degeneration of articular cartilage and subchondral bone in meniscectomy patients, try their best to maintain the normal biomechanical function of the knee joint. Plate transplantation has gradually become a new treatment approach. In this meniscus transplantation, in addition to the type matching of the meniscus transplantation, the reasonable fixation of the meniscus transplantation is another key issue in the transplantation operation. Related studies have confirmed that insufficient fixation of the anterior and posterior angles of the meniscus transplantation will cause Knee function degeneration after meniscus transplantation [7].

Tax risk warning overview
The concept of tax risk and early warning

Tax risk belongs to the category of risk. Before understanding tax risk, it is necessary to clarify what is risk. In 1895, the American scholar Hayes gave a definition of risk from the perspective of economics. He believed that risk is “the possibility of loss”; uncertainty of probability random events is risk. Risks will only occur when there are two or more possibilities for an activity, and the occurrence of risks usually brings some form of loss. Therefore, tax risk is an uncertainty faced by enterprises in all tax-related activities, such as enterprises being inspected by tax authorities, bearing excessive tax liabilities, or incurring liabilities for tax reimbursement and fines. For the production and operation of an enterprise, the pursuit of profit is an eternal theme, but the profit of the enterprise must be controlled within an acceptable risk range. If the profit has a high risk, the enterprise will have the hidden danger of failure [8].

Tax risk has tax uncertainty. Uncertainty is the basis for tax risks. Without uncertainty, risks will not arise, and tax risks will be even more difficult to talk about. In the process of production and operation, enterprises are faced with a variety of decisions. Each decision is the result of a cost-benefit balance. The tax liability is the embodiment of each decision in tax law. Different decisions cause different tax burdens, and even the same decision will have different tax burdens due to different subjective reasons of the taxpayer and objective reasons of the external environment. It should be noted that less tax and delayed taxation have tax risks, and more taxation and early taxation also have tax risks. Less tax payment and delayed tax payment means that failure to pay taxes on time and amount will be punished by tax authorities for late fees and fines, resulting in outflow of economic benefits and reduction of corporate value. By the same token, multiple taxation and early taxation will directly lead to the outflow of economic benefits and time value, reduce corporate value, and cause tax risks.

Stages and characteristics of tax risks

The generation of corporate tax risks is not caused overnight, but is a process of long-term accumulation and gradual development. In the entire development process of corporate tax risks, although these risks will show different tax characteristics, this performance may not be very significant and clear, and some may even be potential, but once it develops rapidly, it will It may enter a complete tax risk state immediately, leading to serious consequences, so the tax risk early warning requires research on the tax-related characteristics exhibited by the enterprise at different stages [9].

The formation of corporate tax risks should be divided into the following four main stages, and exhibit different characteristics. That is: tax risk incubation stage, tax risk development stage, tax risk deterioration stage and tax risk explosion stage. The different characteristics of these four stages can be described with the following figure.

Figure 1

Formation of corporate tax risk

Through the description of the above four stages of tax risk, although not all the companies used have behaved this way most of the companies in financial crisis are similar, and they are widely universal. It's just that different enterprises have different reasons for generating tax risk crises, so the performance of these crisis characteristics are different, or they focus more on the performance of one or more crisis characteristics.

Mechanism analysis of tax risk early warning
Early warning concept of random mode

The stochastic model originated from the study of optimal cash holdings in financial management. In tax risk early warning, this model is also instructive. In the random mode shown in the figure below, the horizontal axis represents time, and the vertical axis represents the size of tax risk. As time changes, tax risk is high and low. For enterprises, risk and return are positively related. The higher the risk, the better, and not the lower the better. Theoretically, there should be an optimal level of tax risk. The constant degree of tax risks can only control tax risks within a feasible range. Assume that the straight-line R is the optimal amount of tax risk for the enterprise, the straight-line H is the upper limit of the tax risk allowed by the enterprise, and the straight-line L is the lower limit of the tax risk that the enterprise is willing to bear. When the tax risk reaches H, the early warning system issues a warning, and the enterprise adjusts the tax risk to the optimal position R. When the tax risk reaches L, the early warning system also issues an alarm, and the enterprise adjusts the tax risk to the state R.

Figure 2

Early warning concept of random mode

Objectives of the tax risk early warning mechanism

As a kind of management behaviour of an enterprise, the tax risk early warning mechanism should serve the overall objective of the enterprise-maximizing the value of the enterprise. As mentioned earlier, because the situation of each enterprise is different, it is impossible to force each enterprise to establish a sound tax risk early warning mechanism. When considering whether and how to establish a tax risk early warning mechanism, we should pay attention to the actual situation of the enterprise and Consider the cost-benefit principle. In order to understand the realization of the objectives of the tax risk early warning mechanism, the following three questions need to be answered: First, should the enterprise establish a tax risk early warning mechanism? Second, how complete should the tax risk warning mechanism itself be? Third, what level should the tax risk early-warning mechanism control the tax risk of the enterprise? Figure 3 shows the scheme of tax risk early warning mechanism [10].

Figure 3

Tax risk early warning mechanism scheme

Convergence and Stability of Ordinary Differential Equation Algorithm dxdy=f(x,y),x[a,b] {{dx} \over {dy}} = f\left({x,y} \right),\,x \in \left[{a,b} \right] y(x0)=y0 y\left({{x_0}} \right) = {y_0}

The general form of the explicit one-step method of the above formula is yn+1=yn+hφ(xn,yn,h)n=0,1,,N1 \matrix{{{y_{n + 1}} = {y_n} + h\varphi \left({{x_n},{y_n},h} \right)} \hfill & {n = 0,1, \cdots,\,N - 1} \hfill \cr}

Where h=baN h = {{b - a} \over N} , xn = a + nh,. In this way, we use the solution yn of the initial value problem (3) of the difference equation as the approximate value of the solution y(xn) at x = xn, that is, y(xn) ≈ yn. Therefore, the solution of y(x+h)y(x)hφ(x,y(x),h) {{y\left({x + h} \right) - y\left(x \right)} \over h} - \varphi \left({x,y\left(x \right),h} \right)

Approach yf(x,y(x))=0 {y^{'}} - f\left({x,y\left(x \right)} \right) = 0

It is possible to approximate the solution to the problem. Therefore, we expect that for any fixed x ∈ [a, b], limh0[y(x+h)y(x)hφ(x,y(x),h)]=0 \mathop {\lim}\limits_{h \to 0} \left[{{{y\left({x + h} \right) - y\left(x \right)} \over h} - \varphi \left({x,y\left(x \right),h} \right)} \right] = 0

If the increment function φ(x, y, h) is continuous with respect to h, then φ(x,y,h)=f(x,y) \varphi \left({x,y,h} \right) = f\left({x,y} \right)

If relation φ(x,y,h)f(x,y) \varphi \left({x,y,h} \right) \ne f\left({x,y} \right)

If it is true, it is said that the one-step method (3) is compatible with the initial value problem of differential equations, as shown in Figure 4 [11].

Figure 4

Comparison of Euler method and modified Euler method

It is easy to verify that both the Euler method and the improved Euler method satisfy the compatibility conditions. In fact, for the Euler method, the incremental function is φ(x,y,h)=f(x,y) \varphi \left({x,y,h} \right) = f\left({x,y} \right)

The compatibility condition is naturally satisfied, and the incremental function of the improved Euler method is φ(x,y,h)=12[f(x,y)+f(x+h,y+hf(x,y))] \varphi \left({x,y,h} \right) = {1 \over 2}\left[{f\left({x,y} \right) + f\left({x + h,y + hf\left({x,y} \right)} \right)} \right]

Because f(x, y), Thus having φ(x,y,h)=12[f(x,y)+f(x,y)]=f(x,y) \varphi \left({x,y,h} \right) = {1 \over 2}\left[{f\left({x,y} \right) + f\left({x,y} \right)} \right] = f\left({x,y} \right)

So, Euler's method and modified Euler's method are compatible with the initial value problem. Generally, if the single-step method is shown to have p-order accuracy (p > 0), its local error is [12] y(x+h)[y(x)+hφ(x,y(x),h)]=O(hp+1) y\left({x + h} \right) - \left[{y\left(x \right) + h\varphi \left({x,y\left(x \right),h} \right)} \right] = O\left({{h^{p + 1}}} \right)

Divide both ends of the above equation by h to get ɛn + 1 → 0 and h → 0. If φ(x, y, h), then y(x)φ(x,y,h)=0 {y^{'}}\left(x \right) - \varphi \left({x,y,h} \right) = 0 which is φ(x,y,h)=f(x,y) \varphi \left({x,y,h} \right) = f\left({x,y} \right)

Therefore, the display single-step method of p > 0 is compatible with the initial value problem. Therefore, the RK method of each order is compatible with the initial value problem. A numerical method is called convergence. If there is any initial value y = 0 and any x ∈ (a, b], limh0yn=y(x)(x=a+nh) \matrix{{\mathop {\lim}\limits_{h \to 0} {y_n} = y\left(x \right)} \hfill & {\left({x = a + nh} \right)} \hfill \cr}

Where y(x) is the exact solution to the initial value problem?

The convergence of a numerical method needs to be determined based on the global truncation error ɛn + 1 of the method. The global truncation error of the known Euler method has an estimated formula |εn+1|hM2L|eL(ba)1|=O(h) \left| {{\varepsilon _{n + 1}}} \right| \le {{hM} \over {2L}}\left| {{e^{L\left({b - a} \right)}} - 1} \right| = O\left(h \right)

When h → 0, ɛn + 1 → 0,, the Euler method converges.

It is assumed that the explicit single-step method has p-order accuracy, and its incremental function φ(x, y, h) satisfies Lipschitz's condition with respect to y. The problem is accurate. If y(x0) = y0, the overall truncation error of the explicit single-step method is en+1=y(xn+1)yn+1=O(hp) {e_{n + 1}} = y\left({{x_{n + 1}}} \right) - {y_{n + 1}} = O\left({{h^p}} \right)

Assuming that the increment function φx, y, h) is continuous over the region S, and that y satisfies the Lipschitz condition, then the sufficient and necessary condition for the explicit one-step convergence is that the compatibility condition holds, that φ(x,y,h)=f(x,y) \varphi \left({x,y,h} \right) = f\left({x,y} \right)

If there are normal numbers h0 and C, such that for any initial starting value y0, y0, the corresponding exact solution yn, yn of the one-step method (18), for all 0 < hh0, there is always |yny˜n|C|y0y˜0|nhba \matrix{{\left| {{y_n} - {{\tilde y}_n}} \right| \le C\left| {{y_0} - {{\tilde y}_0}} \right|} \hfill & {nh \le b - a} \hfill \cr}

It is said that the single step method is stable.

If φ(x, y, h) for x ∈ [a, b], h ∈ (0, h0], and all real numbers y, with respect to lip satisfying the Lipschitz condition, then the one-step method (19) is stable.

For a given differential equation and a given step size h, if there is an error of size δ when calculating yn by the single-step method, then y˜n=yn+δ {\tilde y_n} = {y_n} + \delta is calculated, and the subsequent change of the value ym(m > n) is less than δ, then said that The single step method is absolutely stable [13].

Generally limited to typical differential equations y=μy {y^{'}} = \mu y

Consider the absolute stability of the numerical method, where μ is a complex constant (we are limited to the case where μ is a real number). If for all μh ∈ (α, β), the one-step method is absolutely stable, then (α, β) is called the absolute stability interval. According to the above definition we can The absolute stability interval of Euler's method is E (−2, 0), the absolute stability interval of trapezoidal formula is (−∞, 0), and the absolute stability interval of Runge-Kutta is (−2.78, 0).

The Euler method, improved Euler method, and Runge-Kutta were used to solve the initial value problem. {y=2xy2(0x1.2)y(0)=1 \left\{{\matrix{{{y^{'}} = - 2x{y^2}\left({0 \le x \le 1.2} \right)} \cr {y\left(0 \right) = 1} \cr}} \right.

Figure 5

Euler method, improved Euler method, Runge-Kutta solution for initial value problems

Take equal scores as N = 12, 24, 36, 120, respectively, and calculate the maximum error from the real solution. Euler's method algorithm: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 1.

Maximum error between Euler method numerical solution and real solution

N (Equal score) Maximum error N (equal fraction) Maximum error
12 0.026320 72 0.004052
24 0.012547 84 0.003465
36 0.008233 96 0.003027
48 0.006126 108 0.002687
60 0.004878 120 0.002416

From the running results of the program recorded in Table 1, when the equal score N becomes larger, its error is decreasing. According to the definition we can prove that the method is convergent.

Improved Euler's method: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 2.

Maximum error between the numerical solution and the true solution of the improved Euler method

N (Equal score) Maximum error N (Equal score) Maximum error
12 0.001023 72 0.000028
24 0.000255 84 0.000021
36 0.000113 96 0.000016
48 0.000063 108 0.000013
60 0.000041 120 0.000010

From the program running results recorded in Table 2, when the equal score N becomes larger, its error is decreasing. According to the definition, we can prove that the method is convergent.

Runge-Kutta algorithm: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 3.

Maximum error between Runge-Kutta numerical solution and real solution

N (Equal score) Maximum error N (Equal score) Maximum error
12 0.000001 72 0.000000
24 0.000000 84 0.000000
36 0.000000 96 0.000000
48 0.000000 108 0.000000
60 0.000000 120 0.000000

From the program running results recorded in Table 3, when the equal score N becomes larger, its error is decreasing. According to the definition, we can prove that the method is convergent.

In order to compare the convergence speeds of the above three methods, we have calculated their minimum equal fraction N with an error accuracy of 10-5 as shown in Table 4 below.

Convergence speed comparison

Method N (Minimum grade) Error accuracy
Euler method 2900 10-5
Improved Euler's method 40 10-5
Runge-Kutta method 5 10-5

From the running results of the programs recorded in Table 4, the Runge-Kutta method has the fastest convergence speed, followed by the improved Euler method, and the Euler method is the worst. From this point, the Runge-Kutta method is the most ideal numerical solution among them.

The author believes that the relationship between the tax risk attitude of corporate managers or shareholders and the early warning of tax risks is reflected in the following: Tax risk appetite is willing to accept higher tax risk levels and expect higher returns, and usually sets the threshold for tax risk early warning. Slightly higher; on the contrary, tax risk aversion is willing to bear a lower level of tax risk and can get lower expected returns, generally the tax risk early warning threshold is determined to be more conservative; while the tax risk neutral is between the two [14].

Optimization of supporting conditions for tax risk early warning mechanism
Develop systematic and effective tax risk control procedures
Management attaches importance to tax risk management

If the management of a company ignores tax risk management or believes that there is no tax risk if it operates legally, then the company loses its management basis for tax risk control. Therefore, the support of the manager is the fundamental condition for the company to carry out tax risk management.

Analyse the company's business processes and identify the tax risks it faces.

The company's business process determines the company's applicable taxes, tax rates, tax methods, etc. Therefore, the company's financial staff must analyse the company's business process with the business staff, including: 1, tax analysis of various sales processes; 2, various purchases Analysis of the tax situation of the process; 3. Analysis of the tax situation of special business processes.

Regular audit of company tax and finance

Only by regularly auditing the company's tax, the company can discover the tax issues facing the company in advance, and control the tax risks in the bud. Including: 1, auditing sales and collection business processes; 2, auditing procurement and payment business processes; 3, auditing the authenticity and legality of related documents; 4, auditing the use of related tax benefits; 5, special taxes (personal income tax Stamp duty).

Figure 6

Financial accounting system

Audit company tax before annual settlement

The audit of the company's tax before the annual settlement can adjust the accounting for the problems found in the audit before the annual settlement. The impact of this process on corporate income tax is far-reaching. From the analysis of some previous cases, we have found that cases of overpayment of income tax by the company are not uncommon in practice due to the failure to implement the annual tax pre-check procedures.

Strengthen the company's communication skills in taxation

Don't think that the tax bureau is a bad thing to check the accounts, you must know that the tax staff is responsible for checking the accounts, just like the company employees must go to work. Only by understanding and supporting their work can tax risks be better reduced. In some laws and regulations dealing with ambiguous tax issues, strengthening communication can better solve this problem.

Other supporting conditions for tax risk early warning mechanism

The requirements and changes of the macro-environment are the important reasons that cause enterprises to face tax risks. Therefore, companies should:

Study the macro environment. Although the external macro-environment exists outside the enterprise and cannot be changed, the enterprise can adapt to changes in the environment by adjusting its own operating behaviour. For example, analysis and research on the changing external macro environment, especially analysis and research on national industrial policies, industry policies, relevant laws and regulations, market changes, new products, new technologies, and changes in the international situation, and keep abreast of changes. Understand the trends and laws of the environment, understand and analyse the impact of environmental changes on the production and operation of the enterprise, and fully consider the possibility, severity and impact of changes in the macro environment that make the enterprise face tax risks. If it affects the overall tax burden of the enterprise, how long will the existence of tax risks affect its performance How much influence the indicator has, and so on [15].

Take effective measures. Aiming at the various risks that enterprises may face, on the premise of being proficient in grasping relevant tax-related laws and regulations, and understanding the taxpayer's financial situation and requirements, timely formulate various contingency measures[16], and monitor the development form and status of their production and operation behaviours, Timely feedback. Reflect situations that may occur or are not in line with expectations, and adjust their business goals and implementation processes in a timely manner, in order to reduce the tax risks brought to the enterprise due to the uncertainty of the macro environment through risk prevention and management, and improve risk prevention benefit[17].

Summary

When each early-warning indicator shows different evaluation values, tax risks are in different areas. Enterprises should adopt different strategies to deal with tax risks and control tax risks within an acceptable range. The early warning of tax risks is not the goal of an enterprise. The real purpose of an enterprise is to discover the operating situation of corporate tax risks in a timely manner by means of early warning of tax risks, and use various effective measures to deal with tax risks, and ultimately maximize the value of the enterprise. Of course, the above-mentioned tax risk early-warning mechanism is not a panacea and cannot be applied to every enterprise. Enterprises should make appropriate changes based on the above-mentioned core early-warning indicators according to their own special circumstances, so that the tax risk early-warning mechanism is stubborn. Vitality and broad applicability.

Figure 1

Formation of corporate tax risk
Formation of corporate tax risk

Figure 2

Early warning concept of random mode
Early warning concept of random mode

Figure 3

Tax risk early warning mechanism scheme
Tax risk early warning mechanism scheme

Figure 4

Comparison of Euler method and modified Euler method
Comparison of Euler method and modified Euler method

Figure 5

Euler method, improved Euler method, Runge-Kutta solution for initial value problems
Euler method, improved Euler method, Runge-Kutta solution for initial value problems

Figure 6

Financial accounting system
Financial accounting system

Maximum error between Euler method numerical solution and real solution

N (Equal score) Maximum error N (equal fraction) Maximum error
12 0.026320 72 0.004052
24 0.012547 84 0.003465
36 0.008233 96 0.003027
48 0.006126 108 0.002687
60 0.004878 120 0.002416

Maximum error between the numerical solution and the true solution of the improved Euler method

N (Equal score) Maximum error N (Equal score) Maximum error
12 0.001023 72 0.000028
24 0.000255 84 0.000021
36 0.000113 96 0.000016
48 0.000063 108 0.000013
60 0.000041 120 0.000010

Maximum error between Runge-Kutta numerical solution and real solution

N (Equal score) Maximum error N (Equal score) Maximum error
12 0.000001 72 0.000000
24 0.000000 84 0.000000
36 0.000000 96 0.000000
48 0.000000 108 0.000000
60 0.000000 120 0.000000

Convergence speed comparison

Method N (Minimum grade) Error accuracy
Euler method 2900 10-5
Improved Euler's method 40 10-5
Runge-Kutta method 5 10-5

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