Analytical solution of systems of Volterra integro-differential equations using modified differential transform method
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Authors
Sh. Al-Ahmad
- Faculty of Informatics and Computing , Universiti Sultan Zainal Abidin, Besut Campus, 22200, Kuala Terengganu, Malaysia.
I. B. Sulaiman
- Faculty of Informatics and Computing , Universiti Sultan Zainal Abidin, Besut Campus, 22200, Kuala Terengganu, Malaysia.
M. A. A. Nawi
- School of Dental Sciences, Health Campus, Universiti Sains Malaysia (USM), 16150 Kubang Kerian, Kota Bharu, Kelantan, Malaysia.
M. Mamat
- Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, 22200, Kuala Terengganu, Malaysia.
M. Z. Ahmad
- Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600, Arau Perlis, Malaysia.
Abstract
In this paper, a hybrid technique based on the combining of differential transform approach, the Laplace transformation, and Pade approximant is successfully implemented for solving Volterra Integro differential (VID) equations subject to appropriate conditions. The proposed method known as modified differential transform method (MDTM) enlarges the domain of convergence with less computational time. One of the interesting features of this algorithm is the ability to produce an analytic approximate solution in convergent power series form with few numbers of computable terms. Preliminary results on some test problems show that the new algorithm is efficient and promising for Volterra integro-differential equations and can be applied as alternatives for the integral and integro-differential (IID) equation that have no analytical solution.
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ISRP Style
Sh. Al-Ahmad, I. B. Sulaiman, M. A. A. Nawi, M. Mamat, M. Z. Ahmad, Analytical solution of systems of Volterra integro-differential equations using modified differential transform method, Journal of Mathematics and Computer Science, 26 (2022), no. 1, 1--9
AMA Style
Al-Ahmad Sh., Sulaiman I. B., Nawi M. A. A., Mamat M., Ahmad M. Z., Analytical solution of systems of Volterra integro-differential equations using modified differential transform method. J Math Comput SCI-JM. (2022); 26(1):1--9
Chicago/Turabian Style
Al-Ahmad, Sh., Sulaiman, I. B., Nawi, M. A. A., Mamat, M., Ahmad, M. Z.. "Analytical solution of systems of Volterra integro-differential equations using modified differential transform method." Journal of Mathematics and Computer Science, 26, no. 1 (2022): 1--9
Keywords
- Numerical approximation
- differential transform method
- Volterra integro-differential equations
MSC
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