Numerical Solution of Nonlinear Reaction Diffusion Processes

Numerical Solution of Advection-Diffusion-Reaction Equations

Distributed nonlinear control of diffusion–reaction processes

In this work, we focus on distributed control of quasi-linear parabolic partial differential equations (PDEs) and address the problem of enforcing a prespecified spatio-temporal behaviour in the closed-loop system using nonlinear feedback control and a sufficiently large number of actuators and sensors. Under the assumption that the desired spatio-temporal behaviour is described by a ‘target pa...

Numerical Solution of a Nonlinear Reaction-diffusion Problem in the Case of Hs-regime

Abstract. In this paper, the author propose a numerical method to compute the solution of the Cauchy problem: wt − (w m wx)x = w , the initial condition is a nonnegative function with compact support, m > 0, 1 < p < m + 1. The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a ...

Numerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems

Semilinear reaction-diffusion two-point boundary value problems with multiple solutions are considered. Here the second-order derivative is multiplied by a small positive parameter and consequently these solutions can have boundary or interior layers. A survey is given of the results obtained in our recent investigations into the numerical solution of these problems on layer-adapted meshes.