Numerical Solutions of Some Partial Differential Equations Using Semi-Analytic Methods
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Date
2025
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Facultyof Sciences
Résumé
This work addresses the numerical solution of partial differential equations (PDEs) using semi-analytical
methods. We begin by introducing the fundamental principles of PDEs, laying the groundwork for the
application of advanced solution techniques. A detailed investigation is then carried out on three widely
used semi-analytical methods: the Homotopy Perturbation Method (HPM), the Variational Iteration
Method (VIM), and the Adomian Decomposition Method (ADM). The convergence properties of each
method are analyzed to assess their reliability and effectiveness in solving nonlinear problems. To demonstrate
their practical utility, we apply these methods to the Burgers equation a canonical nonlinear PDE
arising in fluid mechanics. The results confirm that semi-analytical methods provide accurate, efficient,
and easily implementable solutions, offering a robust alternative to purely numerical approaches