Moving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod

Bisheh-Niasar, Morteza; Arab Ameri, Maryam

doi:10.22055/jacm.2017.22854.1141

Moving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod

Document Type : Research Paper

Authors

Morteza Bisheh-Niasar ¹

Maryam Arab Ameri ²

¹ Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran.

² Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

10.22055/jacm.2017.22854.1141

Abstract

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable time steps to protect the positivity condition of the solution. The results of this computational technique are compared with the corresponding uniform mesh non-standard finite difference scheme. The simulations show that the presented method is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh non-standard finite difference fails.

Keywords

Non-standard finite difference

positivity

moving mesh

heat conduction equation

Subjects

Applied Mathematics

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