A Cauchy problem for a one–dimensional diffusion–reaction equation is solved on a grid by a random walk method, in which the diffusion part is solved by random walk of particles, and the (nonlinear) reaction part is solved via Euler’s polygonal arc method. Unlike in the literature, we do not assume monotonicity for the initial condition. It is proved that the algorithm converges and the rate of...

In this paper, we implement Regular Perturbation Method (RPM) of the Solving fractional diffusion-reaction equation, in order to determine exact analytical solutions some linear equation. general, solving using method allow obtain or approximate solutions. For case diffusion and diffusion-convection equations solved document, obtained are exact. By comparing these with those by other researcher...

The kinetic rate equation for the photosensitized cleavage reaction of surface-bound photolabile chromophores with free diffusion of sensitizer molecules from the bulk of a solution to the surface is derived by determining the stationary solution of a diffusion equation with suitable boundary conditions. The relation between the phenomenological rate constant for the photosensitized reaction at...

We solve an optimal control problem governed by evolution equation using bilinear regular feedback. Using optimization techniques, we show how to approximate the flow of a reaction-diffusion system desired target. For application, consider regional constrained distributed system. The paper ends example illustrating numerical approach proposed method.