A Method for Solving a Class of Boundary Value Problems of Laguerre Equation

Li Ren¹, Shunchu Li^1, and Dongdong Gui²

¹School of science, Xihua University, Chengdu, China

²Beijing Dongrunke Petroleum Technology Co.,Ltd., Beijing 100029, China

Cite this paper:
Li Ren, Shunchu Li and Dongdong Gui. A Method for Solving a Class of Boundary Value Problems of Laguerre Equation. American Journal of Applied Mathematics and Statistics. 2015; 3(3):89-92. doi: 10.12691/ajams-3-3-1

Abstract

Based on the analysis of the boundary value problem of Laguerre equation, this paper studies the similar structure of its solution expression. This paper is found that its solution can be obtained by combining similar kernel function with coefficients of left boundary condition. While the similar kernel function is constructed by both the function of guide solution and coefficients of right boundary condition. Hence, we proposed a method for solving this class of boundary value problems: the similar constructing method.

Keywords:
Laguerre equation boundary value problem similar kernel function the similar constructing method

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Zongrong Cheng, Shunchu Li. The Similar Structure Method Solving the Boundary Value Problem of Bessel Equations (in Chinese)[J]. Journal of Sichuan Normal University (Natural Science), 2011,34(6): 850-853.
[2]	Junchao Wang, Shunchu Li. The Similar Structure of Solutions of Second-Order Linear Homogeneous Differential Equation (in Chinese)[J]. Pure Mathematics, 2012, 2(1): 23-27.
[3]	Shunchu Li, Zhi-Jian Liao. Constructing the Solution of Boundary Value Problem of the Differential Equation with it’s an Arbitrary Non-trivial Solution (in Chinese) [J]. Journal of Sichuan University (Natural Science Edition), 2012,49(6):1209-1213.
[4]	Rongjun Huang, Shunchu Li, Dongxu Xu. Similar Structured Method of Solution to Boundary Value of First Weber Equation (in Chinese)[J]. Journal of Mianyang Normal University, 2012, 31(11):1-5(-15).
[5]	Xitao Bao, Shunchu Li, ZhiJian Liao. Similar Constructive Method of Solution for the Boundary Value Problem of Euler Hyper-geometric Differential Equation (in Chinese)[J]. Journal of Southwest University of Science and Technology, 2012, 27(4):101-105.
[6]	Shunchu Li. The Similarity Structuring Method of Boundary Value Problems of the Composite Differential Equations (in Chinese) [J]. Journal of Xihua University (Natural Science Edition), 2013, 32(4): 27-31.
[7]	Congyin Fan, Shunchu Li, Dongxu Xu. Similar Structure Method of Solution of a class of Thomson Equation Boundary Value Problem (in Chinese)[J]. Advances in Applied Mathematics, 2012, 1(2): 41-48.
[8]	Fu-rong Wang, Shunchu Li, Dongxu Xu. The Similarity Construction Method of a Kind of Boundary-Value Problem of Airy Equation(in Chinese) [J]. Journal of Hubei Normal University (Natural Science), 2013, 33(1):79-85.
[9]	Zhijian Liao, Shunchu Li. A new method for solving the boundary value problem of extend Bessel equation: The similar structuring method [J].Journal of University of Science and Technology of China, 2013,43(12):975-979.
[10]	Shunchu Li. The Formal Similarity of Solutions in the Laplace Space on the Class of Partial Differential Equation System (in English)[J]. Journal of Xihua University (Natural Science Edition), 2007, 26(4):83-86.
[11]	Minhui Jia, Shunchu Li. The Formal Similarity of Solutions in the Laplace Space on the Class of Fluid Flow Differential Equation [J]. Journal of Electronic Science and Technology of China, 2005, 3(2):172-174.
[12]	Shunchu Li, Jianjun Zhang. Similar Structure of Pressure Distribution in the Fractal Dual Porosity Reservoir (in Chinese)[J]. Journal of Xihua University (Natural Science Edition), 2006, 25(1):40-43.
[13]	Li Xu, Shunchu Li, Cuicui Sheng. Similar Structure of Flow Effective Well Radius Model through Homogeneous Reservoir Solutions (in Chinese)[J]. Journal of Chongqing Normal University (Natural Science Edition), 2011, 28(4):32-34.
[14]	Xuxia Xiao, Shunchu Li. The Similar Structure of Solutions for the Boundary Value Problem of Euler’s Hypergeometric Differential Equation (in Chinese)[J]. Journal of Inner Mongolia Normal University (Natural Science Edition), 2012, 41(6): 597-600(-603).
[15]	Shishi Liu, Shida Liu. The special function[M]. Beijing: China Meteorological Press, 2002.