Restricted additive Schwarz algorithm for a θ finite difference method to solve a two-dimensional 4th-order partial differential equation with variable coefficient

  • Chadi CHAHID Faculty of Sciences, University of Meknes, Morocco
  • Yassin KHALI Laboratory of Mathematics and Interactions, Faculty of Sciences and Techniques, Moulay Ismail University
  • Samir KHALLOUQ Laboratory of Mathematics and Interactions, Faculty of Sciences, Moulay Ismail University
  • Nabila NAGID Laboratory of Mathematics, Modeling and Automatic Systems, Faculty of Sciences Semlalia, Cadi Ayyad University.
DOI: https://doi.org/10.19139/soic-2310-5070-3021
Keywords: Thin plate, 4th-order partial differential equation,, Finite differences method, Stability analysis, Convergence analysis, Domain decomposition methods, Restricted additive Schwarz, Preconditioning, Parallel computing

Abstract

This paper deals with a θ finite difference scheme to solve two-dimensional 4th-order partial differential equation with variable coefficient, which governs the transverse vibrations of a thin plate.First we establish some a priori estimates for the weak solution of our problem.Then, we introduce a new variable, allowing us to convert the plate equation into a system of two second-order differential equations.Stability and convergence analysis are carried out by employing the energy estimate method.We present a class of domain decomposition methods (DDM) called restricted additive Schwarz (RAS). This method is used as a preconditioner for the GMRES algorithm to solve systems of linear equations arising from the discretization of the plate equation by the present scheme.Numerical experiments are provided, confirming the effectiveness of the algorithms.
Published
2026-03-03
How to Cite
CHAHID, C., KHALI, Y., KHALLOUQ, S., & NAGID, N. (2026). Restricted additive Schwarz algorithm for a θ finite difference method to solve a two-dimensional 4th-order partial differential equation with variable coefficient. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3021
Issue
Online First
Section
Research Articles
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