Application Of Radial Basis Functions Method In Numerical Solution Of Fractional Differential Equations

Fractional differential equations are a class of differential equations obtained by replacing the derivatives of classical integer order differential equations with fractional derivatives.In practical application,fractional order equation can simulate natural phenomena more accurately than integer order equation.In this paper,we mainly discuss the application of radial basis function method in fractional differential numerical solutions.For the sake of simplicity,in this paper,we elaborate the situation for fractional derivative a in the range of 0<?<1 and 1<?<2,based on the fractional diffusion equation and the fractional order convection diffusion equation,it should be noted that this algorithm is still valid for other similar types of equations.First,we use the difference method to separate the time derivative of fractional order.In this paper,we use a discrete form of Crank-Nicolson similar to integer order to construct an unconditional stable time-discrete scheme,and discuss the approximation ability of this discrete format.Then,the radial basis function is used to approximate the space derivative,and the iterative algorithm is obtained.Compared with the traditional methods of finite difference,our algorithm with fewer nodes can get satisfactory approximation ability,in order to verify the effectiveness of the algorithm,the last part of the algorithm is implemented using MATLAB programming.