Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Professor Huang Jianfei, Yangzhou university
Inviter:
唐贻发
Title:
Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations
Time & Venue:
2017.10.28 14:30-15:30 N702
Abstract:
In this talk, two second-order convolution quadrature methods are presented to numerically solve a class of time-space fractional diffusion-wave equations with nonlinear source. For avoiding to discretize the temporal Caputo derivative directly and improving the numerical stability, the fractional diffusion-wave equations are firstly transformed into their equivalent partial integro-differential equations. Then, a second-order convolution quadrature suggested by Lubich is applied to approximate the Riemann-Liouville integral, the deduced convolution quadrature method can handle the solution with low regularity in time. And then, another second convolution quadrature method is proposed based on a new second-order approximation for discretizing the Riemann-Liouville integral at time $t_{k-\frac{1}{2}}$, which reduces the computational complexity when Crank-Nicolson technique is used. The stability and convergence of these two new methods are rigorously proved and discussed. Numerical experiments arecarried out to demonstrate thetheoretical results and efficiencies of our methods.