The Galerkin-Implicit Methods for Solving Nonlinear Hyperbolic Boundary Value Problem

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Jamil A. Ali Al-Hawasy Nuha Farhan Mansour

Abstract

This paper is concerned with finding the approximation solution (APPS) of a certain type of nonlinear hyperbolic boundary value problem (NOLHYBVP).  The given BVP is written in its discrete (DI) weak form (WEF), and is proved that  it has a unique APPS, which is obtained via the mixed Galerkin finite element method (GFE) with implicit method (MGFEIM) that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS).  In this part, the predictor and the corrector technique (PT and CT) are proved convergent and are used to transform the obtained GNAS to  linear (GLAS ), then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are studied. The results are given by figures and shown the efficiency and accuracy for the method

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How to Cite
ALI AL-HAWASY, Jamil A.; MANSOUR, Nuha Farhan. The Galerkin-Implicit Methods for Solving Nonlinear Hyperbolic Boundary Value Problem. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 34, n. 2, p. 119-128, apr. 2021. ISSN 2521-3407. Available at: <https://jih.uobaghdad.edu.iq/index.php/j/article/view/2618>. Date accessed: 31 july 2021.
Section
mathematics