In this presentation, we describe an implicit Closest Point Method [3] which allows large, stable time steps for high-order PDEs while retaining the principal benefits of the original method. Example computations (including the in-surface heat equation, reaction-diffusion on surfaces, Laplace–Beltrami eigenmodes, and fourth-order interface motion) on a variety of surfaces demonstrate the effect...

This paper deals with the effects of partial differential equations on development spatiotemporal patterns in reaction–diffusion systems. These systems describe how concentration a certain substance is distributed space or time under effect two phenomena: chemical reactions different substances into some other product and diffusion which results dispersion over surface space. Mathematical repre...

We consider the reaction-diffusion equation with discontinues coefficients and singular sources in one dimension. In this work, we construct ε-uniformly convergent High Order Compact (HOC) monotone finite difference schemes defined on a priori Shishkin meshes, which have order two, three and four except for a logarithmic factor. Numerical experiments are presented and discussed.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to...

To model biochemical systems in which both noise in the chemical reaction process and spatial movement of molecules is important, both the reaction-diffusion master equation (RDME) and Smoluchowski diffusion-limited reaction (SDLR) partial differential equation (PDE) models have been used. In previous work we showed that the solution to the RDME may be interpreted as an asymptotic approximation...