SEMI-ANALYTICAL METHOD FOR SOLVING ONE DIMENSIONAL HEAT EQUATION

Authors:

Gurpreet singh,Pankaj,

DOI NO:

https://doi.org/10.26782/jmcms.spl.12/2025.08.00003

Keywords:

Variational iterative method,one-dimensional Heat equation,Numerical examples,Laplace transform,

Abstract

The Laplace Transform method and variational iterative approach are combined to create a new semi-analytical methodology that is used in this research to solve one-dimensional heat equations. To illustrate the effectiveness and precision of the suggested approach, numerical results are provided.

Refference:

1. Arife, A. S., and A. Yildirim. “New Modified Variational Iteration Transform Method (MVITM) for Solving Eighth-Order Boundary Value Problems in One Step.” World Applied Sciences Journal, vol. 13, no. 10, 2011, pp. 2186–2190.
2. Douglas, J., and D. W. Peaceman. “Numerical Solution of Two Dimensional Heat Flow Problems.” AIChE Journal, vol. 1, no. 4, 1955, pp. 505–512.
3. Hammouch, Z., and T. Mekkaoui. “A Laplace-Variational Iteration Method for Solving the Homogeneous Smoluchowski Coagulation Equation.” Applied Mathematical Sciences, vol. 6, no. 18, 2012, pp. 879–886.
4. He, J. H. “Variational Iteration Method—A Kind of Non-Linear Analytical Technique: Some Examples.” International Journal of Non-Linear Mechanics*, vol. 34, no. 4, 1999, pp. 699–708.
5. Hesameddini, E., and H. Latifizadeh. “Reconstruction of Variational Iteration Algorithms Using the Laplace Transform.” *International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 11-12, 2009, pp. 1377–1382.
6. Khuri, S. A., and A. Sayfy. “A Laplace Variational Iteration Strategy for the Solution of Differential Equations.” Applied Mathematics Letters, vol. 25, no. 12, 2012, pp. 2298–2305.
7. Kouatchou, J. “Finite Difference and Collocation Methods for Solution of Two Dimensional Heat Equation.” Numerical Methods for Partial Differential Equations, vol. 17, no. 1, 2001, pp. 54–63.
8. Luga, T., T. Aboiyar, and S. O. Adee. “Radial Basis Function Methods for Approximating the Two Dimensional Heat Equations.” International Journal of Engineering Applied Sciences and Technology, vol. 4, no. 2, 2019, pp. 7–15.
9. Murphy, C. P., and D. J. Evans. “Chebyshev Series Solution of Two Dimensional Heat Equation.” Mathematics and Computers in Simulation, vol. 23, no. 2, 1981, pp. 157–162.
10. Shah, R., H. Khan, D. Baleanu, P. Kumam, and M. Arif. “A Semi-Analytical Method for Solving Family of Kuramoto-Sivashinsky Equations.” Journal of Taibah University for Sciences, vol. 14, no. 1, 2020, pp. 402–411.
11. Singh, G., and I. Singh. “New Laplace Variational Iterative Method for Solving 3D Schrödinger Equations.” Journal of Mathematical and Computational Science, vol. 10, no. 5, 2020, pp. 2015–2024.
12. Wu, G. C. “Variational Iteration Method for Solving the Time-Fractional Diffusion Equations in Porous Medium.” Chinese Physics B, vol. 21, no. 12, 2012.

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