This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

We consider a rather general class of convection–diffusion equations, involving dissipation (of possibly fractional order) which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models, Burgers’ equation, the Navier–Stokes equations, the surface quasigeostrophic equations and the Keller–Segel model for chemotaxis. Here we establish a P...

A nonstiff additive semi-implicit third-order Runge-Kutta scheme suitable for integration of convection-diffusion-reaction equations with few diffusion dominated species is presented in this article. This scheme permits larger time steps than those required by explicit schemes and uses only one implicit stage and two explicit stages. The stability domain is analyzed and tests are carried out fo...

In this article we study the convergence and the error bound for the solution of the convection diffusion reaction equation using overlapping Schwarz wave form relaxation method combined with the first order fractional splitting method (Strang’s splitting) as basic solver. We extended the study to solve decoupled and coupled system of equations of same class in order to demonstrate the effect o...

In this paper, the system of ordinary differential equations arisen from discretizing the convection-diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered. This system involves in computing ey for some vector y, where k is the time step-size and A is a large tridiagonal Toeplitz matrix. The common ways to compute an approximat...

In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L∞(J̄ , L(Ω)-norm are obtained. Keywords—Convectio...

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also pre...