Unified solution for the Legendre equation in the interval [−1, 1]—An example of solving linear singular-ordinary differential equations
| Autor: | Jian Ma, Qing-Hua Zhang, Yuanyuan Qu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Applied Mathematics
Weak solution Mathematical analysis 010103 numerical & computational mathematics Legendre's equation 01 natural sciences Legendre function 010101 applied mathematics Computational Mathematics symbols.namesake Associated Legendre polynomials Singular function Singular solution symbols 0101 mathematics Legendre's constant Legendre polynomials Mathematics |
| Zdroj: | Applied Mathematics and Computation. 289:311-323 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2016.05.028 |
| Popis: | This study adopts the corrected Fourier series expansion method with only limited smooth degree to solve the Legendre equation with an arbitrary complex constant µ, and finds general solution for the intervals 0, 1 and -1, 0, which includes a logarithm singular function in forms of ln ( 1 - x ) and ln ( 1 + x ) , respectively, and a nonsingular function. The smooth conjunction of these two portions at x=0 constructs the unified solution for the Legendre equation in the interval -1, 1. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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