TY - JOUR
TI - A novel numerical manner for non-linear coupled variable order reaction-diffusion equation
AU - Kashif Mohd
AU - Pandey Prashant
AU - Jafari Hossein
JN - Thermal Science
PY - 2023
VL - 27
IS - 101
SP - 353
EP - 363
PT - Article
AB - In this work, an efficient variable order Bernstein collocation technique,  which is based on Bernstein polynomials, is applied to a non-linear coupled  system of variable order reaction-diffusion equations with given initial  and boundary conditions. The operational matrix of Bernstein polynomials is  derived for variable order derivatives w.r.t. time and space. The Bernstein  operational matrix and collocation technique are applied to the concerned  non-linear physical model to achieve a system of non-linear algebraic  equations, which are further solved by using Newton method. A few examples  are presented to demonstrate the accuracy and stability of the scheme by  comparing L2 and L∞ norm errors between the obtained numerical solutions and  existing solutions. The important feature of this article is the graphical  exhibitions of the effects of variable order derivatives on the solutions of  the considered non-linear coupled reaction-diffusion equation for different  particular cases.