Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 263–273
Temimi-Ansari Method for a Class of Fifth-Order Korteweg-De Vries Equations
Khaled Mohammed Shwish, Ahmed Fawaz Idrees and Harith Fawaz Hazim
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Abstract
In this study examines the application of the Tamimi-Ansari method (TAM) as a semi-analytical iterative approach to solving three different models of nonlinear PDEs derived from fifth-order generalized Korteweg-de Vries (KdV) equation. The method relies on generating approximate solutions in the form of polynomial series and, in some cases, can yield the exact solution depending on the formula of the equation to be solved and the initial condition chosen for this purpose. The method's efficiency and accuracy were evaluated using numerical criteria to measure error and to assess the convergence of approximate and exact solutions. The numerical results demonstrated that the TAM possesses excellent convergence characteristics and high numerical stability and proved its ability to produce accurate approximate solutions for higher-order nonlinear equations. Furthermore, graphical comparisons showed a high degree of agreement between the approximate and exact solutions, confirming the method's effectiveness and reliability in handling this type of PDE.
Keywords
Temimi-Ansari Method Lax Equation Kaup-Kupershmidt Equation Sawada-Kotera Equation
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