Quasilinear singular perturbation problems and the uniform \(L_ 1\)- convergence. (English) Zbl 0684.34058

Vulanović, R.

Z. Angew. Math. Mech. 69, No. 4, T130-T132 (1989).

Quasilinear singularly perturbed boundary value problems are solved numerically by finite-difference schemes of Lax-Friedrichs type. The convergence of the numerical solution towards the discretization of the continuous solution is investigated in the discrete \(L_ 1\)-norm. Sufficient conditions are given under which the convergence is uniform in the perturbation parameter.

Reviewer: R.Vulanović

MSC:

34E15	Singular perturbations, general theory for ordinary differential equations
65L10	Numerical solution of boundary value problems involving ordinary differential equations

Keywords:

uniform convergence; Quasilinear singularly perturbed boundary value problems; finite-difference schemes; numerical solution