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Clavero, Carmelo; Lisbona, Francisco

Uniformly convergent finite difference methods for singularly perturbed problems with turning points. (English) Zbl 0790.65074

Numer. Algorithms 4, No. 4, 339-359 (1993).
A family of finite difference schemes including the upwind method, Samarskij’s method and exponential fitting type methods are studied for finding the approximate solution of one-dimensional singular perturbation problems with turning points. Uniform convergence of the upwind method on irregular meshes is established. Many examples are given to illustrate the efficiency of the proposed methods.
Reviewer: M.A.Noor (Riyadh)

Cited in 8 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations

Keywords:

exponential fitting methods; uniform convergence; finite difference schemes; upwind method; Samarskij’s method; singular perturbation; turning points
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References:

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