The Galerkin-Implicit Method for Solving Nonlinear Variable Coefficients Hyperbolic Boundary Value Problem

  • Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Nuha Farhan Mansour Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Keywords: nonlinear hyperbolic boundary value problem, Galekin finite element method, implicit method; convergence, stability

Abstract

This paper has the interest of finding the approximate solution (APPS) of a nonlinear variable coefficients hyperbolic boundary value problem (NOLVCHBVP).  The given boundary value problem is written in its discrete weak form (WEFM) and proved  have a unique solution, which is obtained via the mixed Galerkin finite element with implicit method that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS). In this part, the predictor and the corrector techniques (PT and CT, respectively) are proved at first convergence and then are used to transform  the obtained GNAS to a linear GLAS . Then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are studied. Some illustrative examples are used, where the results are given by figures that show the efficiency and accuracy for the method.

Published
2021-11-30
How to Cite
Al-Hawasy, J. A. A., & Mansour, N. F. (2021). The Galerkin-Implicit Method for Solving Nonlinear Variable Coefficients Hyperbolic Boundary Value Problem. Iraqi Journal of Science, 62(11), 3997-4005. https://doi.org/10.24996/ijs.2021.62.11.20
Section
Mathematics