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A finite difference approach for solution of Burgers’ equation. (English) Zbl 1093.65081

Summary: We apply a restrictive Pade approximation classical implicit finite difference method to the Burgers’ equation with a set of initial and boundary conditions to obtain its numerical solution. The stability region and truncation error of the new method are discussed. The accuracy of the proposed method is demonstrated by the two test problems. The numerical results obtained by this method for various values of viscosity are compared with the exact solution to show the efficiency of the method. The numerical results are found in good agreement with the exact solutions.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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