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The Elzaki Transform Method for Addressing Cauchy Problems in Higher Order Nonlinear PDEs

Tarig M. ELZAKI

Tarig M. ELZAKI

Department of Mathematics, University of Jeddah, College of Science and Arts El KamelJeddah, Saudi Arabia
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ELZAKI, Tarig M.
 and 
Mohamed Ali LATRACH

Mohamed Ali LATRACH

University of Tunis El Manar, National Engineering School at TunisLamsin, Tunisia
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LATRACH, Mohamed Ali
  
Jun 06, 2025
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Published Online: Jun 06, 2025
Page range: 225 - 231
Received: Dec 07, 2024
Accepted: Mar 03, 2025
DOI: https://doi.org/10.2478/ama-2025-0028
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© 2025 Tarig M. ELZAKI et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1.

Graphical representation of the ETM solution to example 1 after only one iteration
Graphical representation of the ETM solution to example 1 after only one iteration

Fig. 2.

Graphical representation of the exact solution to example 2 via ETM after only one step
Graphical representation of the exact solution to example 2 via ETM after only one step

Fig. 3.

Graphical representation of the exact solution to example 3 via ETM after only one iteration
Graphical representation of the exact solution to example 3 via ETM after only one iteration

Fig. 4.

Graphical representation of the exact solution to example 4 via ETM after only two iterations
Graphical representation of the exact solution to example 4 via ETM after only two iterations

Fig. 5.

Graphical representation of the exact solution to example 5 via ETM after only one iteration
Graphical representation of the exact solution to example 5 via ETM after only one iteration

Relative errors concerning example 4

Point Elzaki relative error
(0,0) 0
(–2, –2) 0
(2, 2) 2.4040 × 10−16
(0.5, 1.8333) 0
(0.5, –1.8333) 1.7360 × 10−15
(1.5, 1.5) 2.6424 × 10−16
(–1.5, –1.5) 3.3171 × 10−16
(1.1667, 0.6667) 1.8535 × 10−16
Language:
English
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4 times per year
Journal Subjects:
Engineering, Electrical Engineering, Electronics, Mechanical Engineering, Mechanics, Bioengineering and Biomedical Engineering, Biomechanics, Civil Engineering, Environmental Engineering
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