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A comparative study of numerical solutions of a class of KdV equation. (English) Zbl 1143.65078
Summary: We present a comparative study of a meshless method, modified Bernstein polynomials and a B-spline finite element method for the numerical solution of two different models of the Korteweg-de Vries (KdV) equation. The multiquadric and Gaussian radial basis functions (RBFs) are used due to an exponential convergence rate. Excellent agreement is found between exact and RBFs solutions and the same accuracy is obtained for Bernstein polynomials and the B-spline finite element method.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
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