APPLICATION OF THE GALERKIN-SBA METHOD TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

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Résumé

In this article, we propose a numerical framework referred to as the Galerkin-SBA method, obtained by coupling the Galerkin projection technique with the SBA iterative approach. The method reduces a nonlinear partial differential equation to a finite-dimensional system governing the time-dependent coefficients in a Galerkin expansion of the solution.
The resulting system is efficiently handled using the SBA procedure, which improves the treatment of nonlinear terms and enhances computational performance. Under suitable assumptions, we establish the convergence and uniqueness of the proposed scheme.

Mots-clés

Galerkin method, SBA method, nonlinear partial differential equations