B-spline collocation algorithm for numerical solution of the generalized Burger’s-Huxley equation. (English) Zbl 1276.65062

Mohammadi, Reza

Numer. Methods Partial Differ. Equations 29, No. 4, 1173-1191 (2013).

The cubic B-spline collocation scheme is implemented to find numerical solutions of the generalized Burger’s-Huxley equation. The scheme is based on the finite-difference formulation for time integration and cubic B-spline functions for space integration. Convergence of the scheme is discussed through standard convergence analysis. The proposed scheme is of second order convergent. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are compared with other results given in literature.

Reviewer: Wilhelm Heinrichs (Essen)

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

cubic B-spline method; collocation; generalized Burger’s-Huxley equation; convergence; numerical results; finite-difference

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