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Implicit finite difference scheme for singularly perturbed Burger-Huxley equations. (English) Zbl 1499.65399

Summary: In this paper, an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation. The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation. The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique. This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration. The derivatives are replaced by finite difference approximation, then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction. The convergence analysis of the proposed method has been established. Numerical experiments were conducted to support the theoretical results. Further, the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35B25 Singular perturbations in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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