Boundary Characteristics Orthogonal Polynomials

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...

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Bibliographic Details
Published in:Advanced Numerical and Semi-Analytical Methods for Differential Equations pp. 45 - 52
Main Authors: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
Format: Book Chapter
Language:English
Published: United States Wiley 2019
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Edition:1
Subjects:
boundary characteristic orthogonal polynomials
boundary value problem
Galerkin's method
Gram‐Schmidt orthogonalization procedure
orthogonal polynomials
Rayleigh‐Ritz method
Linear systems
Boundary conditions
Approximation algorithms
Calculus
Method of moments
Standards
ISBN:9781119423423, 1119423422
Online Access:Get full text
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Summary: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.
ISBN:9781119423423
1119423422
DOI:10.1002/9781119423461.ch4