TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover

Journal of Interdisciplinary Mathematics

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

Powered by:Powered by

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Interdisciplinary Mathematics
Open Access Research Article

Solutions for some integral equations by variation iteration adomain decomposition method

* ,

* Corresponding author · click or hover a name for details

pp. 1415–1420Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1559XML
Published Online:
28 Oct 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1559
Pages:
1415–1420

Abstract

The major aim of this work is to propose a novel method, the Variation Iteration Adomain Decomposition Method (VIADM), an iterative semi-analytical method to achieve an approximate analytical solution for nonlinear (Volterra / Fredholm) integral equations. This technique depends on applying the Adomain Decomposition Method (ADM) to a nonlinear term that can be solved using Adomain polynomials. The VIADM has been used to break down the Volterra integral equation solution into infinite components. Furthermore, some illustrative examples are given, and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability. 

Keywords

Semi-analytical methodAdomain decomposition methodAdomain polynomialsVolterra / fredholm integral equations

Subject Classifications

31A1031B10

References

[1] Abbasbandy S. and Shevanian E., Application of the Variational Iteration Method to Nonlinear Volterra Integro-Differential Equations, Z. Natur for sch, 63a, pp. 538-542 (2008). 
[2] Ali S. M., Some Approximate Solutions of Fractional Integro-Differential Equations, M.Sc., Thesis, AL-Nahrain University, (2010). 
[3] Alao S.,  Akinboro F. S., Akinpelu F. O. and Oderinu R. A., Numerical Solution of Integro-Differential Equation Using Adomian Decomposition Method and Variational Iteration Method. IQSR Journal of Mathematics, 10, pp. 18-22 (2014). 
[4] Erfanian H. R. and Mostahsan T., Approximate solution of Class of Nonlinear Volterra Integral Equations. The Journal of Mathematics and Computer Science, 3, pp. 278-286 (2011). 
[5] Gachpazan M., Numerical Scheme to Solve Integro-Differential Equations System, Journal of Advanced Research in Scientific Computing, 1, pp. 11-21 (2009). 
[6] Rashidinia J. and Tahmasebi A., Approximate Solution of Linear Integro-Differential Equations by Using Modified Taylor Expansion Method, World Journal of Modeling and Simulation, 9, pp. 289-301 (2013). 
[7] Wazwaz A.M., The Variational Iteration Method for Solving Linear and Nonlinear ODEs and Scientific Models with Variable Coefficients, Central European Journal of Engineering, 4, pp. 64-71 (2014). 
[8] Venkatesh S. G., Ayyaswamy S. K. and Balachandar S. R., Legendre Approximate Solution for a Class of Higher-Order Volterra Integro-Differential Equations. Ain Shams Engineering Journal, 3, pp. 417-422 (2012).
[9] HH Omran, Solutins of Systems for the Linear Fredholm-Volterra Integral Equations of the Second Kind, Ibn AL-Haitham Journal For Pure and Applied Science, 23, 2, pp.200-206 (2017).
[10]  Zubain, N. A., & Hussain, A. K. (2022). New Types of Continuous Function and Open Function. Wasit Journal of Computer and Mathematics Sciences, 1(2), 55-61.
[11] Liton Jude Rozario & Md. Imdadul Islam (2009) Performance estimation of call admission control schemes based voice/data integrated wireless cellular network with customer retrials, Journal of Discrete Mathematical Sciences and Cryptography, 12:3, 253-294, DOI: 10.1080/09720529.2009.10698235. 

Views: 188Downloads: 79Citations: 0