The Journal of the Indian Mathematical Society

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Laplace Decomposition Methods for Solving Certain Class of Differential-Difference Equations


Affiliations
1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570006, India
     

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Laplace decomposition methods are based on Laplace transform method and Adomian decomposition method or modified Adomian decomposition method. In this paper we show that the methods are applicable to the class of successive interval valued linear as well as nonlinear differential-difference equations with the differential order two and the difference order one involving a two variable function admitting Taylor series expansion. Two test problems are selected to illustrate the applicability of methods. In both the problems, when the difference parameter w = 0, the resulting differential equations have exact solution. The exact solution is used to compare approximate solutions obtained by Laplace decomposition methods. Numerical results show good convergence of approximate solutions.

Keywords

Differential-Difference Equation, Laplace Decomposition Method, Laplace Transform Method, Modified Adomian Decomposition Method, Successive Interval Valued Problem.
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  • Laplace Decomposition Methods for Solving Certain Class of Differential-Difference Equations

Abstract Views: 222  |  PDF Views: 0

Authors

R. Rangarajan
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570006, India
S. R. Ananth Kumar
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570006, India

Abstract


Laplace decomposition methods are based on Laplace transform method and Adomian decomposition method or modified Adomian decomposition method. In this paper we show that the methods are applicable to the class of successive interval valued linear as well as nonlinear differential-difference equations with the differential order two and the difference order one involving a two variable function admitting Taylor series expansion. Two test problems are selected to illustrate the applicability of methods. In both the problems, when the difference parameter w = 0, the resulting differential equations have exact solution. The exact solution is used to compare approximate solutions obtained by Laplace decomposition methods. Numerical results show good convergence of approximate solutions.

Keywords


Differential-Difference Equation, Laplace Decomposition Method, Laplace Transform Method, Modified Adomian Decomposition Method, Successive Interval Valued Problem.

References