We present a family of novel explicit numerical methods for the diffusion or heat equation
with Fisher, Huxley and Nagumo-type reaction terms. After discretizing the space variables …

We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear
diffusion–reaction equation. The reaction term is a function of time and space …

We collected 20 explicit and stable numerical algorithms for the one-dimensional transient
diffusion equation and analytically examined their consistency and convergence properties …

In this work, we used three finite difference schemes to solve 1D and 2D convective diffusion
equations. The three methods are the Kowalic–Murty scheme, Lax–Wendroff scheme, and …

The time-dependent diffusion equation is studied, where the diffusion coefficient itself
depends simultaneously on space and time. First, a family of novel, nontrivial analytical …

This paper constructs highly accurate and efficient time integration methods for the solution
of transient problems. The motion equations of transient problems can be described by the …

This paper aims to simulate the time-development of the temperature of phase change
materials (PCMs) using an effective heat capacity model. We employ recently published and …

Based on many previous experiments, the most efficient explicit and stable numerical
method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last …

We consider an inverse problem of recovering the mortality rate in the honey bee difference
equation model, that tracks a forage honeybee leaving and entering the hive each day. We …

We investigate diffusion equations which have concentration dependent diffusion
coefficients with physically two relevant Ansätze, the self-similar and the traveling wave …