Numerical solution for the variable order linear cable equation with Bernstein polynomials

In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order fractional linear cable equation. In this paper, we adopted Bernstein polynomials basis defined on the interval [0,R][0,R] to solve the equations defined on the section Ω=[0,X]×[0,T]Ω=[0,X]×[0,T]. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the initial equation is transformed into the products of several dependent matrixes which can also be viewed as the system of linear equations after dispersing the variable. By solving the linear system of algebraic equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.