KHOUDER, IkramSLIMANI ,Ali2025-11-252025-11-252025http://dspace.univ-skikda.dz:4000/handle/123456789/5505This 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 approachesenThesis