Abstract
This paper focuses on a numerical study of the general time-space variable-order fractional nonlinear problem of thermoelasticity in one dimension using the weighted average nonstandard finite difference (WANSFD). By replacing the second order space derivative with a Riesz fractional variable-order derivative and the time derivative by Caputo fractional variable-order operator in the standard system which arises in thermoelasticity, we obtain this general system. Using a kind of John von Neumann technique, we study the stability of the designed schemes. Also, the truncation error of the introduced schemes is studied. Our numerical treatment is shown graphically. These results expose that WANSFD approach is suitable and effective for solving the proposed system; moreover, it is easy to implement.
Highlights
Today scientists in different fields such as plasma waves, fluid mechanics systems and solid state physics use coupled partial differential equations to describe many phenomena
(2020) 2020:288 found the solution of a nonlinear system of coupled hyperbolic and parabolic equations with specified harmonic displacement at the border depending on the Poincaré extension with a small parameter
The fundamental aim of the present article is to carry out numerical treatment of the time-space variable-order fractional differential model (1) which arises in fractional variable-order thermoelasticity using the weighted average nonstandard finite difference (WANSFD) technique
Summary
Today scientists in different fields such as plasma waves, fluid mechanics systems and solid state physics use coupled partial differential equations to describe many phenomena. A system of nonlinear coupled hyperbolic and parabolic equations is always used in studies of circled fuel reactor, radiation hydrodynamics, magnetoelasticity, thermoelasticity, and in biology [1,2,3,4,5]. It is known that studying the behavior of solutions of these systems is a very important and difficult area of research. The authors of [7] and of the references therein studied a system of coupled parabolic equations. In [3], the authors (2020) 2020:288 found the solution of a nonlinear system of coupled hyperbolic and parabolic equations with specified harmonic displacement at the border depending on the Poincaré extension with a small parameter
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