多项分数阶常微分方程的数值积分法

Numerical integration method for multiple fractional ordinarydifferential equationsAbstract In recent years,fractional calculus has been used to solve various problemswith genetic and memory characteristics in physics,materials,mechanics,informationand other fields,as well as to establish various mathematical models.In this paper,Riemann-Liouville fractional integration is used to study and solve the initial value problemof multiple fractional ordinary differential equations.The error analysis of the specificsolution based on the explicit method based on the first-order rectangular formula and themethod based on the second-order convolution weight is compared.The numericalintegration method for solving multi-terms fractional-order ordinary differential equation isdiscussed.Before solving the initial value problem,this paper first introduces the definitionand related properties of Riemann Liouville fractional integral for readers to understand.Two general methods for solving initial value problems of polynomial fractional ordinarydifferential equations are given,which are based on the first order left and right rectangleformula and the second order convolution weight approximation method.In addition,howto use the above two methods to solve the initial value problem of a basic three termfractional ordinary differential equation is demonstrated.The iterative process iscompared according to different steps.The error analysis between the order and theapproximate solution and the exact solution is carried out,and the applicable environmentand the relative advantages and disadvantages of the two methods are evaluated.Hopeto find a new theoretical method to break the existing restrictions and strive to build acomplete set of fractional differential equation theory.Key words Multi-terms fractional-order ordinary differential equation,An explicitmethod based on the first order rectangle formula,Second order convolution weightmethod