Third-order variable-mesh cubic spline methods for singularly-perturbed boundary-value problems

摘要

Third-order variable-mesh methods based on cubic spline approximation for nonlinear singularly perturbed boundary-value problems of the form εy″ = f(x,y), y(a) = α, y(b) = β are presented. The convergence analysis is given and the method is shown to have third-order convergence. Several tet examples are solved to demonstrate the efficiency of the method.