Abstract—In this paper, we develop a method to obtain approximate solution of nonlinear heat equation with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to nonlinear partial differential equation. The nonlinear term can easily be handle with the help of Adomian polynomials. We illustrate this technique with the help of three examples and results of the present technique have closed arrestment with approximate solutions obtained with the help of Adomian Decomposition Method (ADM).

Index Terms—Approximate solution, Laplace decomposition method, nonlinear partial differential equations. Adomian decomposition method.

S. Handibag is with department of Mathematics, Mahatma Basweshwar Mahavidyalaya, Latur-413 512, Maharashtra, India (tel.: +919011491162, e-mail: sujitmaths@gmail.com).
B. D. Karande is with Department of Mathematics, Maharashtra Udaygiri Mahavidyalaya, Udgir, India

Cite: Sujit Handibag and B. D. Karande, "Application of Laplace Decomposition Method to Solve Linear and Nonlinear Heat Equation," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 369-371, 2012.