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...
Uložené v:
| Vydané v: | Advanced Numerical and Semi-Analytical Methods for Differential Equations s. 45 - 52 |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Kapitola |
| Jazyk: | English |
| Vydavateľské údaje: |
United States
Wiley
2019
John Wiley & Sons, Incorporated John Wiley & Sons, Inc |
| Vydanie: | 1 |
| Predmet: | |
| ISBN: | 9781119423423, 1119423422 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | 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 |