Operational methods and differential equations with applications to initial-value problems

被引：42

作者：

Dattoli, G.

Srivastava, H. M. ^{[1
]}

Zhukovsky, K.

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[2] Moscow MV Lomonosov State Univ, Fac Phys, Moscow 119899, Russia

[3] ENEA, Ctr Ric Frascati, Grp Fis Teor & Matemat Applicata, Unita Tecn, I-00044 Frascati, Italy

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 184卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

orthogonal polynomials and functions; operational techniques; integral transformations; partial differential equations; Laguerre polynomials; Hermite polynomials; Bessel polynomials; Hermite-Kampe de Feriet polynomials; Gould-Hopper polynomials; heat; wave and transport equations; Gauss-Weierstrass transform; Black-Scholes equation;

D O I：

10.1016/j.amc.2006.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The authors present and develop a general method of operational nature in order to explore and investigate such families of orthogonal polynomials and functions as the classical and generalized Hermite and Laguerre polynomials, as well as their higher-order and multi-index cases. They also consider several applications of these operational techniques to the solutions of a wide class of partial differential equations, including (for example) the heat, wave, and transport equations, some of which involve second-order Laguerre derivatives. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：979 / 1001

页数：23

共 21 条

[1]

Andrews L. C., 1985, SPECIAL FUNCTIONS EN

[2]

[Anonymous], 1974, MATH SCI ENG

[3]

[Anonymous], 1944, TREATISE THEORY BESS

[4]

Appell P., 1926, Fonctions Hypergeometriques et Hyperspheriques: Polynomes d'Hermite