Journal Article10.1137/0727002
A difference scheme for a nonlinear partial integrodifferential equation
TL;DR: In this paper, a difference method for the numerical integration of a nonlinear partial integrodifferential equation is considered, where the integral term is treated by means of a convolution quadrature suggested by Lubich.
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Abstract: A difference method for the numerical integration of a nonlinear partial integrodifferential equation is considered. The integral term is treated by means of a convolution quadrature suggested by Lubich. Some results from Lubich’s discretized fractional calculus play a crucial role in proving consistency. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. A stability result is derived that is applicable to equations and numerical methods far more general than those treated in this paper.
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Citations
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