On the numerical solution of equations with interior and exterior boundary layers on a nonuniform mesh. (English) Zbl 0672.65070

Liseikin, V. D.; Yanenko, N. N.

BAIL III, Proc. 3rd Int. Conf. Boundary and interior layers, Dublin/Ireland 1984, Conf. Ser. 6, 68-80 (1984).

Summary: [For the entire collection see Zbl 0671.00015.]
Numerical methods for the solution of two-point boundary value problems with singular perturbations on a nonuniform mesh are considered. The mesh is defined by means of special coordinate transformation satisfying the condition of uniform boundedness of the derivatives in the new variables. Error estimates of the numerical solutions are given.

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
65L50	Mesh generation, refinement, and adaptive methods for ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
34E15	Singular perturbations, general theory for ordinary differential equations

Keywords:

interior and exterior boundary layers; two-point boundary value problems; singular perturbations; nonuniform mesh; Error estimates