Numerical Method for Time Distributed-Order Diffusion Equations Based on Reproducing Kernel Space

A numerical method for time distributed-order diffusion equations based on reproducing kernel space is proposed. The distributed-order diffusion equations are transformed into a multinomial fractional-order diffusion equation by using the compound trapezoidal formula. To discuss approximate solutions to the fractional-order diffusion equation, we define a class of binary reproducing kernel space and construct an orthonormal basis of the space by Legendre polynomials. Based on the idea of least residue, the numerical method is given and the convergence analysis is carried out. The final numerical experiments verify the accuracy of our method.