An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems. (English) Zbl 0557.65055
The present paper provides the basis for the extension of the results of U. Ascher and the author [SIAM J. Numer. Anal. 20, 537-557 (1983; Zbl 0523.65064)] to more general problems. An analysis of the box and trapezoidal schemes applied to boundary value problems for linear singularly perturbed first order systems with variable coefficients (without turning points) is given. Stability and convergence results are derived for solution of the difference equation arising from the discretization of the mentioned problem. Some numerical results are presented.
Reviewer: P.Chocholatý
MSC:
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 |