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Solving Variable-Coefficient Fourth-Order ODEs with Polynomial Nonlinearity by Symmetric Homotopy Method
Applied and Computational Mathematics
Volume 7, Issue 2, April 2018, Pages: 58-70
Received: Feb. 4, 2018; Accepted: Feb. 24, 2018; Published: Mar. 22, 2018
Authors
Abdrhaman Mahmoud, School of Mathematical Sciences, Dalian University of Technology, Dalian, China; Department of Mathematics, Faculty of Sciences and Technology, Omdurman Islamic University, Omdurman, Sudan
Bo Yu, School of Mathematical Sciences, Dalian University of Technology, Dalian, China
Xuping Zhang, School of Mathematical Sciences, Dalian University of Technology, Dalian, China
Article Tools Abstract PDF (344KB)
Abstract
In this paper, the eigenfunction expansion method (EEM) is applied to find numerical solutions for variable-coefficient fourth-order ordinary differential equations (ODEs) with polynomial nonlinearity. The symmetry of the solution set for the resulting system of polynomial equations obtained from EEM of the problem is analyzed. The symmetric homotopy method is constructed to calculate all solutions of the discretization system for the problem. Due to the exploitation of symmetry, the number of computations is reduced. Numerical examples are presented to demonstrate the efficiency of the presented homotopy method.
Keywords
Fourth-Order ODEs, System of Polynomial Equations, Homotopy Continuation Method, Numerical Algebraic Geometry, Symmetry Group
Abdrhaman Mahmoud, Bo Yu, Xuping Zhang, Solving Variable-Coefficient Fourth-Order ODEs with Polynomial Nonlinearity by Symmetric Homotopy Method, Applied and Computational Mathematics. Vol. 7, No. 2, 2018, pp. 58-70. doi: 10.11648/j.acm.20180702.14
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