Numerical solution of nonlinear ordinary differential equation for a turning point problem
The authors consider the nonlinear differential problem \(\varepsilon^ 2u''+xa(u)u'-b(x)u=f(x)\), \(0<x<1\), with homogeneous Dirichlet conditions at the boundary. Assuming \(a(u(x))\geq a_ 0>0\) and \(b(x)\geq b_ 0 > 0\) some useful estimations for the solution \(u\) and its derivatives are obtained. On this base the uniform convergence of an exponential fitted difference scheme is proved by usual techniques. The paper ends with an illustrating example.
scientific article; zbMATH DE number 61707