Third-order variable-mesh cubic spline methods for singularly-perturbed boundary-value problems
Third-order variable-mesh methods based on cubic-spline approximation for nonlinear singularly perturbed boundary value problems of the form \(\varepsilon y''= f(x,y)\), \(y(a) = \alpha\), \(y(b) = \beta\) are presented. The convergence analysis is given and the method is shown to have third- order convergence. Several test examples are solved to demonstrate the efficiency of the method.
nonlinear singularly perturbed boundary value problems
scientific article; zbMATH DE number 519672