A Study of Applied Reduced Differential Transform Method Using Volterra Integral Equations in Solving Partial Differential Equations

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Abstract: Nowadays, integration is one of the trending fields applied in calculus, especially in partial differential equations. Researchers are contributing to support useful utilities to solve partial differential equations in many kinds of methods. In this paper, we perform an application of Volterra Integral Equations in a reduced differential transform method (we call VIE-RDTM) to find the approximate solutions of partial differential equations. The aim is to find the approximate solutions approach to the exact solutions with more general forms. We also extend some new results for basic functions and compare the solutions using the reduced differential transform method and VIE-RDTM by depicting the approximate solutions in some partial differential equations. The results showed that the VIE-RDTM method gets the state-of-the-art general form of the solutions when the errors approach zero.

Equations, E-ISSN: 2944-9146, Volume 3, 2023, Art. #11

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Nguyen Minh Tuan, "A Study of Applied Reduced Differential Transform Method Using Volterra Integral Equations in Solving Partial Differential Equations," Equations, vol. 3, pp. 93-103, 2023, DOI:10.37394/232021.2023.3.11
Nguyen Minh Tuan. A Study of Applied Reduced Differential Transform Method Using Volterra Integral Equations in Solving Partial Differential Equations. Equations. 2023;3:93-103. 10.37394/232021.2023.3.11
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