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Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method. (English) Zbl 1242.65209
Summary: A numerical method is proposed to approximate the solution of the nonlinear Burgers’ equation. The method is based on collocation of modified cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply modified cubic B-splines for spatial variable and derivatives which produce a system of first order ordinary differential equations. We solve this system by using the SSP-RK43 or SSP-RK54. These methods need less storage space that causes less accumulation of numerical errors. The numerical approximate solutions to the Burgers’ equation are computed without transforming the equation and without using the linearization. Illustrative eleven examples are included to demonstrate the validity and applicability of the technique. Easy and economical implementation is the strength of this method.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
65L06Multistep, Runge-Kutta, and extrapolation methods
65M30Improperly posed problems (IVP of PDE, numerical methods)
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