We give the analytical solutions of the fractional diffusion equations in one-, and two-
dimensional space described by the Caputo left generalized fractional derivative. We …

Alternating direction implicit (ADI) orthogonal spline collocation schemes are formulated and
analysed for a class of partial integro-differential equations of parabolic type. These …

In this paper, we develop an efficient splitting domain decomposition method (S-DDM) for
compressible contamination fluid flows in porous media over multiple block-divided sub …

In this paper, we develop and analyze the efficient splitting domain decomposition method
for solving parabolic equations. The domain is divided into non-overlapping multi-block …

The initial boundary value problem for the 3D convection-diffusion equation corresponding
to the mathematical model of suspended matter transport in coastal marine systems and …

We study space and time discretizations for mixed formulations of parabolic problems. The
spatial approximation is based on the multipoint flux mixed finite element method, which …

We discuss the Crank–Nicolson and Laplace modified alternating direction implicit
Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient …

A new family of linearly implicit fractional step methods is proposed and analysed in this
paper. The combination of one of these time integrators with a suitable spatial discretization …

In this article, a new unconditionally stable scheme, based on the Associated Hermite
orthogonal functions combined with first-order upwind scheme (AH-FUS), is proposed for …

This work deals with the efficient numerical solution of a class of nonlinear time-dependent
reaction–diffusion equations. Via the method of lines approach, we first perform the spatial …