Numerical Methods For The Time Fractional Fokker-Planck Equation

This paper studies the numerical algorithms for the time fractional Fokker-Planck equation.On the one hand, this paper combines the Predictor-Corrector approach withthe technique of variable-step. According to the specified local truncation errorto adjust the length of time-step. This method can satisfy the specified errorand e?ectively reduce the computation cost. Numerical examples show that themethod is e?ective.On the other hand, this paper constructs another numerical algorithm forthe time fractional Fokker-Planck equation. This method transform the frac-tional di?erential equations to the fractional integral equation, then use centraldi?erence to approach first-order and second-order partial derivatives, and usepiecewise linear interpolation to approach the integral parts. Here we gives theanalysis of local truncation error and the stability of this method. Numericalexamples demonstrate the method is e?ective.