Solutions of Volterra Integral Equations (VIEs) of the Second Kind with Bulge Function using Aboodh Transform

  • Asif Iqbal Ali Department of Mathematics, National College of Business Administration and Economics, main campus Lahore 54660, Pakistan.
  • Muhammad Kalim Department of Mathematics, National College of Business Administration and Economics, main campus Lahore 54660, Pakistan.
  • Adnan Khan Department of Mathematics, National College of Business Administration and Economics, main campus Lahore 54660, Pakistan.
Keywords: Aboodh Transformation Method (ATM), bulge function, convolution theorem, improved Simpsons method, Taylor series expansion, Volterra integral equations (VIEs)

Abstract

A large class of complexities in mathematical physics, applied mathematics, and engineering are expressed as differential equations with few additions and certain conditions. This research focuses on the solution of Volterra integral equations (VIEs) of the second kind, with bulge functions as known functions. To obtain an analytical solution, the Aboodh transform, the Aboodh inverse transform, and the convolution theorem are employed, since it is required to discover the precise solution of VIEs. This solution is compared with a numerical solution using the modified Simpson method. Finally, it is represented graphically.

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References

. K.S. Aboodh. (2013). The New integral transform “Aboodh Transform” Global Journal of Pure and Applied Mathematics, 9(1),35-43.

K.S. Aboodh, (2014). Application of new transform “Aboodh transform” to partial differential Equation, Global Journal of pure and applied Math, 10 (2), 249-254.

A. M. wazwaz. (2011). Linear and nonlinear integral Equations: Method and applications. Springer.

H Jafari, M Ghorbani, and S Ghasempour. (2013).A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences, 2:22-26.

A V Kamyad, M Mehrabinezhad, and J S Nadjafi.(2010). A numerical approach for solving linear and nonlinear Volterra integral equations with controlled error. International Journal of Applied Mathematics, 40:1-6.

D Bahuguna, A Ujlayan, and D N Pandey. (2009). A comparative study of numerical methods for solving an integrodifferential equation. Computers and Mathematics with Applications, 57:1485-1493

A V Kamyad, M Mehrabinezhad, and J S Nadjafi.(2010). A numerical approach for solving linear and nonlinear Volterra integral equations with controlled error. International Journal of Applied Mathematics, 40:1-6.

F.Mirzaee, (2012). A computational method for solving linear Volterra integral equations, AMS., 6(17), 807-814.

M.M. Rahman, M. A. Hakim, M. Kamrul Hasan, M. K. Alam and L. Nowsher Ali,(2012). Numerical Solution of Volterra integral equations of the 2nd kind with the help of Chebyshev Polynomials, Annals of pure and applied math., 1(2), 158-167.

P. Haarsa and S. Pothat.(2015). A bulge function on Volterra integral equations of the second kind by using the Laplace transform. AMS. 9(1), no.45-50.

Lokenath Debnath and D. Bhatta. (2006). Integral transform and their application second Edition, Chapman and hall/CRC.

Asif Iqbal Ali, M.I.Bhatti, (2015).” Comparison of Aboodh Transformation and Differential Transformation Method Numerically”. Science International Lahore (Pakistan), Vol. 27(2), pp.873-87.

Asif Iqbal Ali ,M.Kalim and Adnan Khan (2021). ‘’Effect of Aboodh Adomian Method for the Solution of Nonlinear Integro Differential and Volterra Integeral Equations Based on Newton Raphson Method”., LC International Journal of Stem, Volume :2(2) (ISSN:2708-7123), 13–22, https://doi.org/10.5281/zenodo.5150178.

Published
2022-05-12
How to Cite
1.
Iqbal Ali A, Muhammad Kalim, Adnan Khan. Solutions of Volterra Integral Equations (VIEs) of the Second Kind with Bulge Function using Aboodh Transform. Sci Inquiry Rev. [Internet]. 2022May12 [cited 2022Dec.5];6(2):21-. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/2067
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Articles