Exponentially fitted finite difference scheme for singularly perturbed two point boundary value problems. (English) Zbl 1319.65065
Summary: In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at left (or right) end of the domain. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that proposed technique provides first order accuracy independent of the perturbation parameter. Several linear and nonlinear problems are solved by the proposed method and numerical results are presented to illustrate the theoretical parameter-uniform error bounds established.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
singular perturbation problems; exponential fitting factor; Thomas algorithm; uniform convergence; finite difference method; two-point boundary value problems; stability; numerical result; error boundReferences:
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