Solving coupled non-linear higher order BVPs using improved shooting method

[1] Azarnavid B., Emamjomeh M., Nabati M., A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem, Chaos Solitons and Fractals, 159, 112159, 2022. AzarnavidB. EmamjomehM. NabatiM. A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem Chaos Solitons and Fractals 159 112159 2022 Search in Google Scholar

[2] Miele A., Well K.H., Tietze J.L., Multipoint approach to the two-point boundary value problem, Journal of Mathematical Analysis and Applications, 44(3), 625–642, 1973. MieleA. WellK.H. TietzeJ.L. Multipoint approach to the two-point boundary value problem Journal of Mathematical Analysis and Applications 44 3 625 642 1973 Search in Google Scholar

[3] Uçar Y., Yağmurlu N.M., Yiğgit M.K., Numerical solution of the coupled Burgers equation by trigonometric B-spline collocation method, Mathematical Methods in the Applied Sciences, 46(5), 6025–6041, 2023. UçarY. YağmurluN.M. YiğgitM.K. Numerical solution of the coupled Burgers equation by trigonometric B-spline collocation method Mathematical Methods in the Applied Sciences 46 5 6025 6041 2023 Search in Google Scholar

[4] Yağmurlu N.M., Gagir A., A finite difference approximation for numerical simulation of 2D viscous coupled Burgers equations, Mathematical Sciences and Applications E-Notes, 10(3), 146–158, 2022. YağmurluN.M. GagirA. A finite difference approximation for numerical simulation of 2D viscous coupled Burgers equations Mathematical Sciences and Applications E-Notes 10 3 146 158 2022 Search in Google Scholar

[5] Yağmurlu N.M., Gagir A., Numerical simulation of two dimensional coupled Burgers equations by Rubin-Graves type linearization, Mathematical Sciences and Applications E-Notes, 9(4), 158–169, 2021. YağmurluN.M. GagirA. Numerical simulation of two dimensional coupled Burgers equations by Rubin-Graves type linearization Mathematical Sciences and Applications E-Notes 9 4 158 169 2021 Search in Google Scholar

[6] Morrison D., Riley J.D., Zancanaro J.F., Multiple shooting method for two-point boundary value problems, Communications of the ACM, 5(12), 613–614, 1962. MorrisonD. RileyJ.D. ZancanaroJ.F. Multiple shooting method for two-point boundary value problems Communications of the ACM 5 12 613 614 1962 Search in Google Scholar

[7] Keller H.B., Numerical Solution of Two Point Boundary Value Problems, Society for Industrial and Applied Mathematics, Philadelphia, USA, 1976. KellerH.B. Numerical Solution of Two Point Boundary Value Problems Society for Industrial and Applied Mathematics Philadelphia, USA 1976 Search in Google Scholar

[8] Matinfar M., Ghasemi M., Solving BVPs with shooting method and VIMHP, Journal of the Egyptian Mathematical Society, 21(3), 354–360, 2013. MatinfarM. GhasemiM. Solving BVPs with shooting method and VIMHP Journal of the Egyptian Mathematical Society 21 3 354 360 2013 Search in Google Scholar

[9] Singh J., A nonlinear shooting method and its application to nonlinear Rayleigh-Bénard convection, International Scholarly Research Notices, 2013(650208), 1–9, 2013. SinghJ. A nonlinear shooting method and its application to nonlinear Rayleigh-Bénard convection International Scholarly Research Notices 2013 650208 1 9 2013 Search in Google Scholar

[10] Javeed S., Shabnam A., Baleanu D., An improved shooting technique for solving boundary value problems using higher order initial approximation algorithms, Punjab University Journal of Mathematics, 51(11), 101–113, 2019. JaveedS. ShabnamA. BaleanuD. An improved shooting technique for solving boundary value problems using higher order initial approximation algorithms Punjab University Journal of Mathematics 51 11 101 113 2019 Search in Google Scholar

[11] Jones D.J., Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems, Journal of Computational and Applied Mathematics, 47(3), 395–400, 1993. JonesD.J. Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems Journal of Computational and Applied Mathematics 47 3 395 400 1993 Search in Google Scholar

[12] Wang H., Ouyang Z., Wang L., Application of the shooting method to second-order multi-point integral boundary-value problems, Boundary Value Problems, 2013(205), 1–10, 2013. WangH. OuyangZ. WangL. Application of the shooting method to second-order multi-point integral boundary-value problems Boundary Value Problems 2013 205 1 10 2013 Search in Google Scholar

[13] Wang H., Ouyang Z., Tang H., A note on the shooting method and its applications in the Stieltjes integral boundary value problems, Boundary Value Problems, 2015(102), 1–11, 2015. WangH. OuyangZ. TangH. A note on the shooting method and its applications in the Stieltjes integral boundary value problems Boundary Value Problems 2015 102 1 11 2015 Search in Google Scholar

[14] Kwong M.K., Wong J.S.W., The shooting method and nonhomogeneous multipoint BVPs of second-order ODE, Boundary Value Problems, 2007(064012), 1–16, 2007. KwongM.K. WongJ.S.W. The shooting method and nonhomogeneous multipoint BVPs of second-order ODE Boundary Value Problems 2007 064012 1 16 2007 Search in Google Scholar

[15] Granas A., Guenther R.B., Lee J.W., The shooting method for the numerical solution of a class of nonlinear boundary value problems, SIAM Journal on Numerical Analysis, 16(5), 828–836, 1979. GranasA. GuentherR.B. LeeJ.W. The shooting method for the numerical solution of a class of nonlinear boundary value problems SIAM Journal on Numerical Analysis 16 5 828 836 1979 Search in Google Scholar

[16] Russell R.D., Shampine L.F., Numerical methods for singular boundary value problems, SIAM Journal on Numerical Analysis, 12(1), 13–36, 1975. RussellR.D. ShampineL.F. Numerical methods for singular boundary value problems SIAM Journal on Numerical Analysis 12 1 13 36 1975 Search in Google Scholar

[17] Sabeh Z., Shamsi M., Navon I.M., An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation, International Journal for Numerical Methods in Fluids, 86(7), 433–453, 2018. SabehZ. ShamsiM. NavonI.M. An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation International Journal for Numerical Methods in Fluids 86 7 433 453 2018 Search in Google Scholar

[18] Burden R.L., Faires J.D., Numerical Analysis, 9th Edt., Brooks/Cole Publishing Company, USA, 1998. BurdenR.L. FairesJ.D. Numerical Analysis 9th Edt. Brooks/Cole Publishing Company USA 1998 Search in Google Scholar

[19] Abbasbandy S., Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation, 145(2–3), 887–893, 2003. AbbasbandyS. Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method Applied Mathematics and Computation 145 2–3 887 893 2003 Search in Google Scholar

[20] Noor K.I., Noor M.A., Iterative methods with fourth-order convergence for nonlinear equations, Applied Mathematics and Computation, 189(1), 221–227, 2007. NoorK.I. NoorM.A. Iterative methods with fourth-order convergence for nonlinear equations Applied Mathematics and Computation 189 1 221 227 2007 Search in Google Scholar

[21] Chun C., A new iterative method for solving nonlinear equations, Applied Mathematics and Computation, 178(2), 415–422, 2006. ChunC. A new iterative method for solving nonlinear equations Applied Mathematics and Computation 178 2 415 422 2006 Search in Google Scholar

[22] Noor M.A., Ahmad F., Javeed S., Two-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 181(2), 1068–1075, 2006. NoorM.A. AhmadF. JaveedS. Two-step iterative methods for nonlinear equations Applied Mathematics and Computation 181 2 1068 1075 2006 Search in Google Scholar

[23] Argyros I., Computational Theory of Iterative Methods, 1–504, Elsevier, New York, USA, 2007. ArgyrosI. Computational Theory of Iterative Methods 1 504 Elsevier New York, USA 2007 Search in Google Scholar

[24] Kou J., The improvements of modified Newton’s method, Applied Mathematics and Computation, 189(1), 602–609, 2007. KouJ. The improvements of modified Newton’s method Applied Mathematics and Computation 189 1 602 609 2007 Search in Google Scholar

[25] Liu L., Wang X., Eighth-order methods with high efficiency index for solving nonlinear equations, Applied Mathematics and Computation, 215(9), 3449–3454, 2010. LiuL. WangX. Eighth-order methods with high efficiency index for solving nonlinear equations Applied Mathematics and Computation 215 9 3449 3454 2010 Search in Google Scholar

[26] Aziz R.C., Hashim I., Alomari A.K., Thin film flow and heat transfer on an unsteady stretching sheet with internal heating, Meccanica, 46(2), 349–357, 2011. AzizR.C. HashimI. AlomariA.K. Thin film flow and heat transfer on an unsteady stretching sheet with internal heating Meccanica 46 2 349 357 2011 Search in Google Scholar

[27] Anjali Devi S.P., Raj J.W.S., Numerical simulation of magnetohydrodynamic forced convective boundary layer flow past a stretching/shrinking sheet prescribed with variable heat flux in the presence of heat source and constant suction, Journal of Applied Fluid Mechanics, 7(3), 415–423, 2014. Anjali DeviS.P. RajJ.W.S. Numerical simulation of magnetohydrodynamic forced convective boundary layer flow past a stretching/shrinking sheet prescribed with variable heat flux in the presence of heat source and constant suction Journal of Applied Fluid Mechanics 7 3 415 423 2014 Search in Google Scholar

[28] Shah F.A., Noor M.A., Waseem M., Some second-derivative-free sixth-order convergent iterative methods for nonlinear equations, Maejo International Journal of Science and Technology, 10(1), 79–87, 2016. ShahF.A. NoorM.A. WaseemM. Some second-derivative-free sixth-order convergent iterative methods for nonlinear equations Maejo International Journal of Science and Technology 10 1 79 87 2016 Search in Google Scholar

[29] Selvakumar K., A computational procedure for solving singular perturbation problems arising in control system using shooting method, International Journal of Computational Science and Mathematics, 3(1), 1–10, 2011. SelvakumarK. A computational procedure for solving singular perturbation problems arising in control system using shooting method International Journal of Computational Science and Mathematics 3 1 1 10 2011 Search in Google Scholar