Solution of boundary value problems for integro-differential equations by using differential transform method

Aytac Arikoglu; Ibrahim Ozkol

doi:10.1016/j.amc.2004.10.009

Solution of boundary value problems for integro-differential equations by using differential transform method

Aytac Arikoglu, Ibrahim Ozkol^*

^*Corresponding author for this work

Department of Aeronautical Engineering

Research output: Contribution to journal › Article › peer-review

215 Citations (Scopus)

Abstract

In this study, we extended the differential transform method (DTM) to solve the integro-differential equations. New theorems for the transformation of integrals are introduced and prooved. The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the method. Some numerical results are also given to demonstrate the superiority of the method to other common techniques. The results we obtained by using this technique is much more accurate compared to the existing ones.

Original language	English
Pages (from-to)	1145-1158
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	168
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2004.10.009
Publication status	Published - 15 Sept 2005

Keywords

Differential transform method
Integro-differential equations
Taylor series

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10.1016/j.amc.2004.10.009

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abstract = "In this study, we extended the differential transform method (DTM) to solve the integro-differential equations. New theorems for the transformation of integrals are introduced and prooved. The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the method. Some numerical results are also given to demonstrate the superiority of the method to other common techniques. The results we obtained by using this technique is much more accurate compared to the existing ones.",

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N2 - In this study, we extended the differential transform method (DTM) to solve the integro-differential equations. New theorems for the transformation of integrals are introduced and prooved. The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the method. Some numerical results are also given to demonstrate the superiority of the method to other common techniques. The results we obtained by using this technique is much more accurate compared to the existing ones.

AB - In this study, we extended the differential transform method (DTM) to solve the integro-differential equations. New theorems for the transformation of integrals are introduced and prooved. The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the method. Some numerical results are also given to demonstrate the superiority of the method to other common techniques. The results we obtained by using this technique is much more accurate compared to the existing ones.

KW - Differential transform method

KW - Integro-differential equations

KW - Taylor series

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Solution of boundary value problems for integro-differential equations by using differential transform method

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Keywords

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