Spectral Collocation Method Analysis And Its Convergence For Time Fractional Nernest-Planck Equation

Fractional differential equations are mainly developed on the basis of physics,they have been widely used in the fields of systems such as biology,chemistry,physics and thermals.Therefore,it is necessary to use a simple and efficient method to obtain the solutions of each fractional differential equation.We know that the development of spectral methods has a long history,and it has become an important tool for calculating high-precision solutions of differential equations.Based on this,the paper uses the spectral collocation method to solve a class of time fractional coupled equation.In this paper,we use Jacobi spectral collocation method to solve the time frac-tional Nernst-Planck equation.Firstly,the fractional equation is transformed into Volterra integral equation with weak singular kernel by using the fractional integral-differential operator definitions and operations,and get the spectral discrete format of the equation,then the convergence of Jacobi spectral collocation method is the-oretically analyzed and proved,we obtain that the error between the exact solution and the approximate solution has exponential attenuation in the L~?and L_?~2 norm.Finally,we verify the correctness of the theoretical analysis through three specific numerical examples,and further prove the feasibility and efficiency of solving the fractional-order Nernst-Planck equation by Jacobi spectral collocation method.