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Convolution quadrature time discretization of fractional diffusion-wave equations. (English) Zbl 1090.65147

The authors present the convolution quadrature time discretization of fractional diffusion-wave equation. They write the integro partial differential equation as an abstract parabolic evolution equation in a Banach space and present convolution quadrature. First the numerical method is considered in the setting of linear nonhomogeneous problems. then they comment on the class of nonlinear problems and the regularity of their solutions. A numerical method for the nonlinear problems is given. Numerical experiments are presented.

MSC:

65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
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