Numerical Method And Derivative Order Estimation Of Coupled Fractional Differential Equations

In the real world,many complex problems are described by cou-pled fractional differential equations,but most coupled fractional dif-ferential equations can not get accurate solutions.For the numerical solution and parameter inversion of nonlinear Caputo fractional differ-ential equation coupling system,the research work of this thesis is as follows:1.Euler method for fractional coupled equations.The initial val-ue problem of coupled fractional differential equations is transformed into an equivalent Volterra integral equation system,and then it is divided into grids.The implicit Euler method is constructed by using the method similar to the integral of numbers,and its convergence and stability are analyzed.The results show that when ?>0,The convergence order of Euler scheme is 1.2.Legendre spectral collocation method for fractional coupled equations.The boundary value problems of coupled fractional differ-ential equations is transformed into an equivalent Fredholm integral equation system.The integral equations are discretized by the spec-tral method based on Legendre polynomials,and the Legendre spectral collocation method for the coupled system of nonlinear fractional dif-ferential equations is constructed,and the error range under the norms of L~2-and L^?-is given.The results show that the Legendre spectral collocation method has good convergence when 1