Two Kinds Of Numerical Methods For Nonlinear Time Fractional Equations

In this article,we study two approximate calculation methods of nonlinear time fractional equations:Galerkin finite element method with WSGD approximation for non-linear modified time fractional diffusion equation and the linear interpolation method for a nonlinear fractional ordinary differential equation.Firstly,the numerical scheme for solving a class of nonlinear time fractional diffusion equation is constructed by combining finite element approximation with WSGD approx-imation.To begin with,we give the numerical scheme,which is formulated by using second-order backward difference approximation for the time integer derivative,WSGD approximation for time fractional derivative.Galerkin finite element method for spatial direction.Furthoer,we derive the proof of the existence and uniquceness of finitce elment solution and prove the L2 error estimates between numerical solution and exact solution.Finally,we provide some numerical results with second-order time convergence rate to test and verify the theoretical analysis.By the numerical calculations,ones also find that the WSGD approximation combined with Galerkin finite element method can significantly improve the convergence pre.cision.Finally.we establish a numerical scheme by using a linear interpolation polynomial method to solve a class of nonlinear ordinary differential equation including the Hadamard finite-part integral.in the time direction.we discretize the fractional derivative in time by linear interpolation polynomial method.and approximate integer time derivative by making use of second-order backward difference scheme.We derive the error results with O(Tmin(1+?,1+3).Moreover,we declare that our theoretical results are correct,by the comparison between the numerical results and the exact results.