Numerical approach of fisher's equation with strang splitting technique using finite element galerkin method

Melike Karta

Article Details

Numerical approach of fisher's equation with strang splitting technique using finite element galerkin method

Authors:

Melike Karta

Publisher:

Yildiz Technical University

Main Topics:

Structural Biology

Journal:

Sigma Journal of Engineering and Natural Sciences Vol.41 Issue 2, pp.344-355

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001311505

pISSN:

1304-7191

Keywords:

Abstract:

 In the present paper, non-linear Fishers reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fishers equation is split into two sub-equations with respect to time such that one is linear and the other one is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check the correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier studies existing in the literature calculating the error norms norms 2   .The solutions obtained in the article show that the present method is quite proper for using many partial differential equations in terms of being easy and conve-nient to computer application.

 In the present paper, non-linear Fishers reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fishers equation is split into two sub-equations with respect to time such that one is linear and the other one is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check the correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier studies existing in the literature calculating the error norms norms 2   .The solutions obtained in the article show that the present method is quite proper for using many partial differential equations in terms of being easy and conve-nient to computer application.

 In the present paper, non-linear Fishers reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fishers equation is split into two sub-equations with respect to time such that one is linear and the other one is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check the correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier studies existing in the literature calculating the error norms norms 2   .The solutions obtained in the article show that the present method is quite proper for using many partial differential equations in terms of being easy and conve-nient to computer application.

 In the present paper, non-linear Fishers reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fishers equation is split into two sub-equations with respect to time such that one is linear and the other one is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check the correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier studies existing in the literature calculating the error norms norms 2   .The solutions obtained in the article show that the present method is quite proper for using many partial differential equations in terms of being easy and conve-nient to computer application.

Article Details

Numerical approach of fisher's equation with strang splitting technique using finite element galerkin method

Authors:

Melike Karta

Publisher:

Yildiz Technical University

Main Topics:

Structural Biology

Journal:

Sigma Journal of Engineering and Natural Sciences Vol.41 Issue 2, pp.344-355

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001311505

pISSN:

1304-7191

Symmetric Strang Splitting

Reaction-Diffusion Equation

Quadratik B-Splines

Finete Element Method

Issues

Article Details

Numerical approach of fisher's equation with strang splitting technique using finite element galerkin method

Authors: Melike Karta

Publisher: Yildiz Technical University

Main Topics: Structural Biology

Journal: Sigma Journal of Engineering and Natural Sciences Vol.41 Issue 2, pp.344-355

Document Type: Article

Publication Date: 4/2023

Document Language: English

Document ID (Org No.): 2001311505

pISSN: 1304-7191

Symmetric Strang Splitting

Reaction-Diffusion Equation

Quadratik B-Splines

Finete Element Method

Issues

Authors:

Melike Karta

Publisher:

Yildiz Technical University

Main Topics:

Structural Biology

Journal:

Sigma Journal of Engineering and Natural Sciences Vol.41 Issue 2, pp.344-355

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001311505

pISSN:

1304-7191