Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Hazrat Ali; Nilormy Gupta Trisha; Md. Shafiqul Islam

Article Details

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Authors:

Hazrat Ali | Nilormy Gupta Trisha | Md. Shafiqul Islam

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.75 Issue 223, pp.88-101

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001614033

pISSN:

2519-9277

Keywords:

Abstract:

 The purpose of the research is to find the numerical solutions to the system of time dependent nonlinear parabolic partial
differential equations (PDEs) utilizing the Modified Galerkin Weighted Residual Method (MGWRM) with the help of modified
Bernstein polynomials. An approximate solution of the system has been assumed in accordance with the modified Bernstein
polynomials. Thereafter, the modified Galerkin method has been applied to the system of nonlinear parabolic PDEs and has
transformed the model into a time dependent ordinary differential equations system. Then the system has been converted into
the recurrence equations by employing backward difference approximation. However, the iterative calculation is performed
by using the Picard Iterative method. A few renowned problems are then solved to test the applicability and efficiency of our
proposed scheme. The numerical solutions at different time levels are then displayed numerically in tabular form and graphically
by figures. The comparative study is presented along with L2 norm, and L∞ norm.

Article Details

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Authors:

Hazrat Ali | Nilormy Gupta Trisha | Md. Shafiqul Islam

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.75 Issue 223, pp.88-101

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001614033

pISSN:

2519-9277

Parabolic PDE System

Modified Galerkin Method

Modified Bernstein Polynomial

Backward Difference Method

Gray-Scott Model

Issues

Article Details

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Authors: Hazrat Ali | Nilormy Gupta Trisha | Md. Shafiqul Islam

Publisher: Refaad for Studies and Research, Jordan

Journal: General Letters in Mathematics Vol.75 Issue 223, pp.88-101

Document Type: Article

Publication Date: 12/2023

Document Language: English

Document ID (Org No.): 2001614033

pISSN: 2519-9277

Parabolic PDE System

Modified Galerkin Method

Modified Bernstein Polynomial

Backward Difference Method

Gray-Scott Model

Issues

Authors:

Hazrat Ali | Nilormy Gupta Trisha | Md. Shafiqul Islam

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.75 Issue 223, pp.88-101

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001614033

pISSN:

2519-9277