Later, the combined application of DQM with an explicit finite difference method(FDM) is presented for the solution of nonlinear reaction-diffusion equation in one- and two-dimensions =-=[3]-=-. There, since an explicit time integration method is used, a relaxation parameter is proposed, in ...
reaction–diffusion equationporous mediaSchauder fixed point theoremfinite difference methodIn this paper, with the help of a variant of Schauder fixed point theorem in the real Banach algebra together with the finite difference method (FDM), we take a brief look at the [Formula: see text]-adic...
Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator Article08 March 2018 Introduction Reaction–diffusion models (RDMs) play a vital role in describing various spatial patterns like mazes, stripes, and spots through chemical ope...
Numerical methods such as Finite Difference Method (FDM) and Finite Element Method (FEM) are widely used to derive the approximate solution of the reaction-diffusion system14,15,16. The current FEM workflow for solving a time-dependent reaction-diffusion system is shown in Fig. 1: (i) generat...
Cells manufactured by FDM 3DP involve multitude of functionalities and have found use in a broad range of electrochemical processes and applications, which are summarized in Table 1. However, none of these cells allows a fundamental analysis of electron transfer processes and related phenomena which ...
Physical model As described by Wanunu et al.28, the transport path of DNA through a nanopore can be divided into five steps: (i) free diffusion to a semi-spherical absorbing boundary, (ii) biased diffusion to the nano- pore, (iii) DNA threading into the nanopore, (iv) DNA translocation...
Finite Difference Method (FDM)Crank-Nicholson (CN)Fourth Order Implicit (FOI)Convection-Diffusion-Reaction (CDR)A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a hi...
The method is based on applying a high-order finite difference method (FDM) to approximate the time Caputo fractional derivative and employing OSC method to approximate the spatial fourth-order derivative. Using the argument developed recently by Lv and Xu (SIAM J. Sci. Comput. 38, A2699-A...
nonlinear reaction–diffusion equationnonlinear wave equationDQMFDMLSMFEMThree different time-integration schemes, namely the finite difference method (FDM) with a relaxation parameter, the least-squares method (LSM) and the finite element method (FEM), are applied to the differential quadrature (DQM)...
advection-diffusion equationsolute transport systemgroundwater contaminationnonlinear reaction termfinite differenceIn the present article, the advection-diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The ...