A uniformly convergent difference scheme for a singularly perturbed problem with convective term and zeroth order reduced equation. (English) Zbl 1051.65081
Summary: A boundary value problem for a linear second-order ordinary differential equation with small parameters by first and the second derivatives is considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form an exponentially fitted difference scheme on a uniform mesh is developed which is shown to be \(\varepsilon\)-uniformly first-order accurate in the \(C(\overline \omega_h)\) norm for original problem. Numerical results are also given.
MSC:
65L12 | Finite difference and finite volume methods for ordinary differential equations |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
34B05 | Linear boundary value problems for ordinary differential equations |
34E15 | Singular perturbations for ordinary differential equations |