Application of Laplace Differential Transform Method in Solving Two-Dimensional Partial Differential Equations with Variable Coefficient

Deborah Oluwatobi Daniel

doi:10.14456/nujst.2022.15

Authors

Deborah Oluwatobi Daniel Department of Mathematics and Computer Science, Faculty of Pure and Applied Sciences, Southwestern University, Ogun State, 110001, Nigeria

DOI:

https://doi.org/10.14456/nujst.2022.15

Keywords:

Nonhomogeneous PDE, 2-D PDE, Laplace Differential Transform Method, Laplace Transform, Differential Transform Method

Abstract

In this paper, Laplace Differential Transform Method (LDTM) is employed in solving two-dimensional partial differential equations with variable coefficients. Laplace Differential Transform Method (LDTM) combines Laplace transform and Differential Transform Method (DTM) and can be used to effectively solve 2-D partial differential equations. In order to demonstrate the effectiveness of this method, 2-D heat-like equations and wave-like equation were considered. Results revealed that the LDTM is effective and efficient in handling 2-D homogeneous and nonhomogeneous partial differential equations with little computational effort.

References

Al-Ahmad, S., Mamat, M., & AlAhmad, R. (2020). Finding differential transform using difference equation. IAENG International Journal of Applied Mathematics, 50, 1-9.

Alquran, M., & Mohammad, M. (2011). Approximate solutions to system of nonlinear partial differential equations using homotopy perturbation method, International Journal of Nonlinear Science, 2, 485-497.

Ganji, H. F., Jouya, M., Mirhosseini-Amiri, S. B., & Ganji, D. D. (2016). Traveling wave solution by differential transformation method and reduced differential transformation method, Alexandria Engineering Journal, 55, 2985-2994.

Ghafoori, M., Motevalli, M. G., Nejad, M. G., Shakeri, F., Ganji, D. D., & Jalaal, M. (2011). Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM, Current Applied Physics, 11, 965-971.

He, J. (2006). Homotopy perturbation method for solving boundary value problem. Physics Letter A, 3, 87-88.

Islam, S., Khan, Y., Faraz, N., & Austin, F. (2010). Numerical solution of logistic differential equations by using the Laplace decomposition method. World Applied Sciences Journal, 8, 1100-1105.

Jafari, H., Chun, C., Seifi S., & Saeidy, M. (2009). Analytical solution for nonlinear Gas Dynamic equation by Homotopy Analysis Method. Application and Applied Mathematics, 4, 149-154.

Moghimi, S. M., Ganji, D.D., Bararnia, H., Hosseini, M., & Jalaal, M. (2011). Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem, Computer and Mathematics with Application, 61, 2213-2216.

Neog, B. C. (2015). Solutions of some systems of non-linear PDEs using Reduced Differential Transform Method. IOSR Journal of Mathematics, 11, 37-44.

Tari, A., & Shahmorad, S. (2011). Differential transform method for the system of two-dimensional nonlinear Volterra integro-differential equations. Computers and Mathematics with Applications, 61, 2621-2629.

Zhou, J. K. (1986). Differential transformation and its application for electrical circuits. Wuhan, China: Huazhong University Press.

Zou, L., Zong, Z., Wang, Z., & Wang, S. (2010). Differential transform method for solving solitary wave with discontinuity, Physics Letter A, 374, 3451.