Year: 2019
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 538–557
Abstract
Two second-order convolution quadrature methods for fractional nonlinear diffusion-wave equations with Caputo derivative in time and Riesz derivative in space are constructed. To improve the numerical stability, the fractional diffusion-wave equations are firstly transformed into equivalent partial integro-differential equations. Then, a second-order convolution quadrature is applied to approximate the Riemann-Liouville integral. This deduced convolution quadrature method can handle solutions with low regularity in time. In addition, another second-order convolution quadrature method based on a new second-order approximation for discretising the Riemann-Liouville integral at time $t$$k$−1/2 is constructed. This method reduces computational complexity if Crank-Nicolson technique is used. The stability and convergence of the methods are rigorously proved. Numerical experiments support the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.230718.131018
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 538–557
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Fractional diffusion-wave equation nonlinear source convolution quadrature generating function stability and convergence.