Tesfa BisetThomas Kebede2025-09-052025-09-052024-10-03https://etd.aau.edu.et/handle/123456789/7372The 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.en-USDecomposition MethodDifferential EquationLaplace-Adomian Decomposition MethodNonlinear Heat EquationsThesis