Boundary Characteristics Orthogonal Polynomials - Chakraverty, Snehashish; Mahato, Nisha; Karunakar, Perumandla; Dilleswar Rao, Tharasi (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
Boundary characteristic orthogonal polynomials (BCOPs) may be generated by using the Gram‐Schmidt orthogonalization procedure. The generated BCOPs have to satisfy the boundary conditions of the considered problem. This chapter presents the Gram‐Schmidt orthogonalization process for generating orthogonal polynomials. From a set of functions, one can construct appropriate orthogonal functions by using the well‐known procedure known as the Gram‐Schmidt orthogonalization process. The first member of BCOPs set is chosen as the simplest polynomial of the least order which satisfies the boundary conditions of the considered problem. The chapter explains how to solve a boundary value problem by using BCOPs with Galerkin's method. It also presents another approach viz. Rayleigh‐Ritz method and solves a boundary value problem by using BCOPs with the Rayleigh‐Ritz method.