Block Unification of Multi-Step Methods for the Solution of Boundary Layer Flow

Abstract

We develop a class of block unification multi-step method (BUMM) which are used as boundary value methods for the numerical integration of third order boundary value problems in ordinary differential equations resulting from boundary layer flow. The method solves the problem directly instead of converting it to a system of first order ordinary differential equations before solving. The block unification multi-step methods are constructed using Chebyshev polynomials as basis function and employing interpolation and collocation method. The basic properties of the methods are investigated and numerical experiments are given to show the performance of the methods.