Laplace Adomian Decomposition Method to Solve Non Linear Partial Differential Equation
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Date
2024-10-03
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Addis Ababa University
Abstract
The Laplace-Adomian Decomposition Method (LADM) is an effective technique for solving nonlinear heat equations, which are crucial in various scientific and
engineering applications. By combining the Laplace transform with Adomian’s Decomposition Method, LADM simplifies the resolution of nonlinearities and boundary conditions, transforming complex equations into manageable subproblems solved iteratively. This approach enhances computational efficiency
and convergence speed without linearization or discretization.
LADM is also successfully applied to the Porous Medium Equation (PME) and Fast Diffusion Equation (FDE), which describe physical processes like fluid
flow through porous media and diffusion. The method demonstrates high accuracy and practicality, making it a valuable tool for tackling complex nonlinear
problems.
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Keywords
Decomposition Method, Differential Equation, Laplace-Adomian Decomposition Method, Nonlinear Heat Equations