BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS IN NUMERICAL APPROXIMATION

The paper describes a procedure to generate boundary characteristic or thogonal polynomials (BCOPs) over a domain in R''. The method is based upon the Gram-Schmidt process of orthogonalization. The orthogonal po lynomial sequence (OPS) is generated from a set of linearly independen t functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R(2), the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosc eles right-angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their nor mal derivatives vanish on the boundary; (c) when no conditions have be en imposed on the boundary. The results for other geometries such as a n ellipse, a parallelogram and an arbitrary triangle follow by some si mple transformations. The procedure is also applicable to one-dimensio nal problems and can be easily extended to R(3).