Mixed Crank-Nicolson and Galerkin Methods for Solving Nonlinear Hyperbolic Partial Differential Equation

Marwa Ahmed; W. A. Ibrahim; S. J. M. Al-Qaisi

Article Details

Mixed Crank-Nicolson and Galerkin Methods for Solving Nonlinear Hyperbolic Partial Differential Equation

Authors:

Marwa Ahmed | W. A. Ibrahim | S. J. M. Al-Qaisi

Publisher:

Mustansiriyah University

Journal:

Mustansiriyah Journal of Pure and Applied Sciences Vol.2 Issue 4, pp.7-18

Document Type:

Article

Publication Date:

9/2024

Document Language:

English

Document ID (Org No.):

2001930704

pISSN:

2957-9910

Keywords:

Abstract:

 In this work,the approximation solution for nonlinear hyperbolic partial differential equation(NLHPDE) is obtained by using the mixed Crank-Nicolson (CN) schemeand the GalerkinMethod(GM) and it is symbolized by (MCNGM).At first theCNis utilized for the variable of time to obtain the discrete weak form for the NLHPDE, and then the GM is utilized which reduces the DWF into theGalerkin nonlinear algebraic system (GNLAS) at each step of time. Through utilizing the predictor-corrector techniques which are symbolized by the obtained GNLAS is transformed into Galerkin linear algebraic system (GLAS) which is solved by applying the Cholesky method. The convergence of the method is studied. Some examples are given to illustrate the efficiency and the accuracy for the proposed method.

Article Details

Mixed Crank-Nicolson and Galerkin Methods for Solving Nonlinear Hyperbolic Partial Differential Equation

Authors:

Marwa Ahmed | W. A. Ibrahim | S. J. M. Al-Qaisi

Publisher:

Mustansiriyah University

Journal:

Mustansiriyah Journal of Pure and Applied Sciences Vol.2 Issue 4, pp.7-18

Document Type:

Article

Publication Date:

9/2024

Document Language:

English

Document ID (Org No.):

2001930704

pISSN:

2957-9910

NonlinearHyperbolicPartial DifferentialEquation

method of Galerkin finite elements

Crank-Nicolson Scheme

Convergent

Issues

Article Details

Mixed Crank-Nicolson and Galerkin Methods for Solving Nonlinear Hyperbolic Partial Differential Equation

Authors: Marwa Ahmed | W. A. Ibrahim | S. J. M. Al-Qaisi

Publisher: Mustansiriyah University

Journal: Mustansiriyah Journal of Pure and Applied Sciences Vol.2 Issue 4, pp.7-18

Document Type: Article

Publication Date: 9/2024

Document Language: English

Document ID (Org No.): 2001930704

pISSN: 2957-9910

NonlinearHyperbolicPartial DifferentialEquation

method of Galerkin finite elements

Crank-Nicolson Scheme

Convergent

Issues

Authors:

Marwa Ahmed | W. A. Ibrahim | S. J. M. Al-Qaisi

Publisher:

Mustansiriyah University

Journal:

Mustansiriyah Journal of Pure and Applied Sciences Vol.2 Issue 4, pp.7-18

Document Type:

Article

Publication Date:

9/2024

Document Language:

English

Document ID (Org No.):

2001930704

pISSN:

2957-9910