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Use of modified Bernstein polynomials to solve KdV-Burgers equation numerically. (English) Zbl 1157.65447

Summary: A numerical solution of the Korteweg-de Vries-Burgers (KdVB) equation is presented using modified Bernstein polynomials (B-polynomials). Over the spatial domain, B-polynomials are used to expand the desired solution requiring a discretization with only the time variable. The Galerkin method is used to determine the expansion coefficients to construct the initial trial functions. We use a fourth-order Runge-Kutta method to solve the system of equations for the time variable. The accuracy of the solutions is dependent on the size of the B-polynomial basis set. Numerical results obtained using this method are compared with existing analytical results. Excellent agreement is found between the exact solution and approximate solution obtained by this method.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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References:

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