Approximate Solution of Fractional Order of Partial Differential Equations Using Laplace-Adomian Decomposition Method in MATLAB (Published)
This article presents the application of the Laplace-Adomian Decomposition Method (LADM) for solving partial differential equations (PDEs) in the context of heat conduction and wave propagation. The LADM combines Laplace transform and Adomian decomposition to approximate solutions to PDEs efficiently in MATLAB. The procedure involves transforming the PDE into simpler differential equations, which are then solved iteratively using the Adomian decomposition method. The advantages of LADM include simplicity, flexibility, and applicability to a wide range of PDEs. We demonstrate the effectiveness of LADM through numerical experiments solving the heat equation and wave equation using MATLAB. The results show good agreement with analytical solutions and highlight the efficiency and accuracy of LADM for solving PDEs.
Keywords: Laplace-Adomian Decomposition Method (LADM) MATLAB, Partial Differential Equations, Visualization, computational methods, numerical solution, one-dimensional heat equation, one-dimensional wave equations, surface plots
SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS USING ACCELERATED GENETIC ALGORITHM (Published)
This project introduced an accelerated method of Genetic Algorithms (GAs) to solve Partial differential equations. This new method for solving partial differential equations, based on grammatical evolution is presented. The method forms generations of trial solutions expressed in an analytical closed form and developed by inserting the boundary conditions, part of exact solution or exact solution as a vectors of trial solutions in the population of the problem. Several examples are worked out and in most cases the exact solution is recovered. When the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. We report results on several problems to illustrate the potential of this approach.
Keywords: Genetic Algorithms (Gas), Nonlinear, Partial Differential Equations