Volume 9, Issue 4
On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters

J. Comp. Math., 9 (1991), pp. 321-329

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• Abstract

We consider the singular perturbation problem $-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0$,u(0),u(1) given with two small lparameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$.The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.

• History

Published online: 1991-09

• Keywords