Solution of non‐linear boundary value problems by discrete least squares

Abstract

Abstract This paper presents a new discrete (point‐matching) least squares method for solving general, non‐linear boundary value problems. The technique uses a mixed formulation and minimizes the sum of squared residuals by Powell's (1965) algorithm. The present method is compared with finite difference and weighted residual finite element methods in the examples and discussion. It shows considerable promise as a general differential equation solver for both large and small computer systems.