The splitting method is a powerful method for solving partial differential equations. Various
splitting methods have been designed to separate different physics, nonlinearities, and so …

In this paper, we consider a class of convection-diffusion equations with memory effects.
These equations arise as a result of homogenization or upscaling of linear transport …

Due to the potential decrease of the computation time for problems with fractional order
derivatives, and due to the extension of the range of applicable solvers for a given problem …

We propose a space and time adaptive framework for a partially explicit splitting scheme of
flow problems in multiscale media. We consider the parabolic equation with high-contrast …

This paper aims to present a robust computational technique utilizing finite difference
schemes for accurately solving time fractional reaction–diffusion models, which are …

Multi-physics are widely studied and used in numerical analysis and simulation. Physics-
based splitting methods are introduced, in which different methods are applied to solve each …

This paper considers flow problems in multiscale heterogeneous porous media. The
multiscale nature of the modeled process significantly complicates numerical simulations …

In this paper, we construct a higher order predictor–corrector technique for time fractional
Benjamin–Bona–Mahony–Burgers' equations. Instead of directly using an explicit scheme …

Solving multiscale diffusion problems is often computationally expensive due to the spatial
and temporal discretization challenges arising from high-contrast coefficients. To address …

In this paper, we introduce an economical technique based on a semi-implicit predictor–
corrector scheme for solving fractional Benjamin–Bona–Mahony–Burgers equations, in …