This article reviews convolution quadrature and its uses, extends the known approximation
results for the case of sectorial Laplace transforms to finite-part convolutions with non …

This paper addresses the numerical solution of the three-dimensional nonlocal evolution
equation with a weakly singular kernel. The first order fractional convolution quadrature …

A class of finite difference methods for solving fractional diffusion equations is considered.
These methods are an extension of the weighted average methods for ordinary (non …

This work formulates two kinds of alternating direction implicit (ADI) schemes for the
parabolic-type three-dimensional evolution equation with a weakly singular kernel. The …

A survey is given on some numerical methods of Riemann-Liouville fractional calculus. The
topics discussed here will be:(a) approximation of fractional derivatives by generalized finite …

This work constructs and analyzes a nonlocal evolution equation with a weakly singular
kernel in three-dimensional space. In the temporal direction, the Crank-Nicolson (CN) …

We propose and analyze a time-stepping Crank-Nicolson (CN) alternating direction implicit
(ADI) scheme combined with an arbitrary-order orthogonal spline collocation (OSC) …

Recently, there has appeared a new type of evaluating partial differential equations with
Volterra integral operators in various practical areas. Such equations possess new physical …

The paper constructs a fast efficient numerical scheme for the nonlocal evolution equation
with three weakly singular kernels in three-dimensional space. In the temporal direction, We …

In this work, we propose and analyze a new method for the solution of the three-dimensional
evolutionary equation with a nonlocal term. Then the method combines Galerkin finite …