Numerical solution of a class of two-dimensional non-linear variable
order fractional reaction-diffusion equations in porous media
Abstract
In the present scientific article, an efficient operational matrix based on
the famous Bernstein polynomials is applied for the numerical solution
of two-dimensional non-linear variable order reaction-diffusion equation
in porous media with given initial and boundary conditions. An
operational matrix is constructed for fractional variable order
differentiation w.r.to space variable x,y and time t, so that our
proposed model is converted into a system of non-linear algebraic
equations with the help of collocation method, which can be solved
employing the Newton-Iteration method. The salient features of the
article are finding the stability analysis and error bounds of the
proposed method and also the validation and the effectiveness of the
method through the RMS, L∞ and L2 errors. The physical presentation of
the these errors for considered twodimensional non-linear variable order
reaction-diffusion with their exact solutions shows the method is too
good for finding the solution of these kind of problems.