79 citations · 263 across the 55 of their papers we have counts for
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Numerical solution of the heat conduction problem with memory
Petr N. Vabishchevich
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory an…
Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
Petr N. Vabishchevich
We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of th…
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels
Petr N. Vabishchevich
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The comp…
Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator
Petr N. Vabishchevich
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical m…
Contrast-independent partially explicit time discretizations for multiscale wave problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung +1
In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale…
Contrast-independent partially explicit time discretizations for multiscale flow problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung +1
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the desi…