New approach for solving of Extended KdV Equation

Ramadan, Motaz; Aly, Hayah

doi:10.21608/ajbas.2022.125893.1093

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2023

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“…The work in paper [34] showed that the new multiple solutions obtained in [33] were actually not new but transformed known solutions of the KdV and KdV-Burgers' equations. A new approach to solve the extended KdV equation was discussed in [35] via the Galerkin finite element method with quintic B-spline functions as weight functions.…”

Section: Introductionmentioning

confidence: 99%

Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions

2023

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This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation. The method is used to solve various cases of Burgers’ equations, including the modified Burgers’ equation. The KdV–Burgers’ equation is considered as a test case for the OCFE method using cubic splines. The results compare favourably with existing results. The stability and convergence of the method are also given consideration. The method is unconditionally stable and second-order accurate in time and space.

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Section: Introductionmentioning

confidence: 99%