We consider initial/boundary value problems for the subdiffusion and diffusion-wave
equations involving a Caputo fractional derivative in time. We develop two fully discrete …

In this article, a finite difference/finite element algorithm, which is based on a finite difference
approximation in time direction and finite element method in spatial direction, is presented …

The main purpose of this work is to study the numerical solution of a time fractional partial
integro-differential equation of Volterra type, where the time derivative is defined in Caputo …

ABSTRACT A novel numerical technique is considered for the solution of a multi-term time-
fractional diffusion equation. The orthogonal spline collocation method is used for in space …

In this article, a fully discrete local discontinuous Galerkin (LDG) method with high-order
temporal convergence rate is presented and developed to look for the numerical solution of …

New numerical techniques are presented for the solution of the two-dimensional fractional
diffusion-wave equation with a time fractional derivative of order α (1< α< 2). In these …

In this paper, a high-order local discontinuous Galerkin (LDG) method combined with
weighted and shifted Grünwald difference (WSGD) approximation is developed and …

The paper aims to develop the stable numerical schemes for generalized time-fractional
diffusion equations (GTFDEs) with smooth and non-smooth solutions on the non-uniform …

In this article, a two-grid block-centered finite difference scheme is introduced and analyzed
to solve the nonlinear time-fractional parabolic equation. This method is considered where …

Higher order non‐Fickian diffusion theories involve fourth‐order linear partial differential
equations and their solutions. A quintic polynomial spline technique is used for the …