时间分数阶微分方程的数值解法

The numerical solution of the time fractionaldifferential equationAbstract With the continuous upgrade of calculation tools in recent years,the application offractional differential equations becomes more widespread in different areas of our life,such asfinancial economics,materials sciences,genetics,physics,and other research fields.Given theobjective situation that the analytical solution of differential equation is not practical,researchers arenow focusing on the numerical solution of fractional differential equation.The main aim of this paperis to introduce a simple and accurate way to solve fractional differential equation,check the accuracyof this arithmetic using MATLAB and conduct error analysis at the end.To better describe this arithmetic,this paper is structured into three parts.The first part mainlydescribes the definition and related theorems of the calculus equation,the derivative of Caputo,Riemann-Liouville integral,calculus operator.The second part introduces the conduction process ofthis arithmetic to solve fractional differential equation.It includes two steps.First,obtain theequivalent equation using related theorems of calculus operator.Then discrete equation usingdiscrete approximation.The third part is conducting numerical experiment to solve time fractionaldifferential equation in order to verify the effectiveness of this arithmetic as well as conducting erroranalysis.The result of numerical experiment shows,compared with the approximating solution,the exactsolution has a little error value,the effectiveness of the method is verified.Key words fractional differential equations,Caputo derivative,Riemann-Liouville integrals,numerical approximation,linearization第页