Browsing by Author "Thomas Kebede"

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    Laplace Adomian Decomposition Method to Solve Non Linear Partial Differential Equation
    (Addis Ababa University, 2024-10-03) Thomas Kebede; Tesfa Biset
    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.