多项分数阶常微分方程的数值微分法

Numerical differentiation of fractional order ordinary differential equationAbstract In recent years,the numerical differentiation of multiple fractional ordinary differentialequations has played a very important role in many fields of mathematical models,and also has animportant significance in life and many fields of science and engineering.And the numericaldifferentiation method of multiple fractional ordinary differential equations is also a very important partthat many researchers and scholars have been trying to study in recent years.In this paper,we mainly study and solve the numerical differential problems of many fractionalorder ordinary differential equations by the method of function approximation.Before we solve theproblems by the method of function approximation,we need to understand many definitions offunction approximation.Finally,we study the numerical differentiation of multiple fractional ordinarydifferential equations.I divided this paper into three parts.The first part mainly introduces the relateddefinitions and properties,including the definition and properties of function approximation and thesolution of nonlinear equation.In the second part,we mainly discuss the numerical differentiationmethod of the multiple fractional ordinary differential equations.Through our preliminary knowledge,we use the numerical solution based on L1 approximation and the linear numerical solution based onL1 approximation.Then we can continue to solve the numerical solution of the numerical exampleand the exact solution to prove the correctness and effectiveness of the algorithm.The third part isthe specific code of MATLAB..KEY WORDS:Function approximation,ordinary differential equation,numerical differential method,nonlinear equation