Similar Constructing Method for Solving the Boundary Value Problem of the Composite Thomson Equation

Authors

  • Xiao Xu Dong College of Science, Southwest Petroleum University, Chengdu, 610500, China
  • Zhi Bin Liu College of Science, Southwest Petroleum University, Chengdu, 610500, China
  • Duo Zhang College of Science, Xihua University, Chengdu, 610039, China
  • Shun Chu Li College of Science, Xihua University, Chengdu, 610039, China

DOI:

https://doi.org/10.53555/nnms.v3i4.554

Keywords:

Boundary value problem, Composite Thomson equation, Similar Constructing Method, Similar kernel function, Function of guide solution

Abstract

Based on the theory of similar structure of solution of the boundary value problem of differential equation, this paper studies the solution of a class of boundary value problem of the composite Thomson equation, After analysis? it is indicate that the solution with a form of continued fraction product is obtained by introducing functions of guide solution, constructing similar kernel functions and assembling coefficients of the left non-homogeneous boundary condition, functions of guide solution and similar kernel functions in this paper. Then a new method is obtained for solving the composite boundary value problem——Similar Constructive Method. Furthermore, the function solution is clearly illustrated by the chart which is carried out by the corresponding program in MTLAB. Thus, the method is not only simple and effective for solving the complicated boundary value problem of differential equation, but also is a kind of innovation of ideological.

References

Li S. C., Preliminary Exploration and Prospects of the Similar Structure of Solutions of Differential Equations (in Chinese) [J].Journal of Xihua University (Nature Science Edition). 2010,29(2):223-226(to 238)

Fan C.Y., Li S. C., Xu D.X., Similar Constructive Method of Solution for a Class of Boundary Value Problem of Thomson Equation (in Chinese) [J]. Advances in Applied Mathematics, 2012,1(2):41-48

Li S. C., Liao Z.J., Constructing the Solution of Boundary Value Problem of the Differential Equation with its an Arbitrary Non-trivial Solution (in Chinese) [J]. Journal of Sichuan University (Natural Science Edition), 2012, 49(6):1209-1213

Li S. C., Wu X.Q., 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

Li S. C., The Similarity Structuring Method of Boundary Value Problems for Composite Differential Equations (in Chinese) [J]. Journal of Xihua University (Natural science Edition), 2013,32(1):23-26

Li Q.Y., Li S.C., Li W., Wang J.C., Study of the Nonlinear Fluid Flow Modle in Dual-porosity Media Reservoir Based on Similar Structure (in Chinese) [J]. Chinese Journal of Engineering Mathematics, 2013, 30(1): 123-130

Fan C.Y., Li S.C., Dong X.X., Bai L.X., Algorithms Design Based on Similar Structure (in Chinese) [J]. Advances in Applied Mathematics, 2013,2(3):107-113

Dong X.X., Li S.C., Gui D.D., Pu J., Li H.C., Similar Constructing Method for Solving the Boundary Value Problem of the Composite First Weber system (in Chinese) [J]. American Journal of Applied Mathematics and Statistics, 2013,1(4),76-82

Liu S.S., Liu S.D., Special Function [M]. Beijing: China Meteorological Press, 2002, 50-67

Published

2016-04-30

How to Cite

Dong, X. X., Liu, Z. B., Zhang, D., & Li, S. C. (2016). Similar Constructing Method for Solving the Boundary Value Problem of the Composite Thomson Equation. Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 3(4), 01-08. https://doi.org/10.53555/nnms.v3i4.554

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