A comparison between different numerical methods which are used to solve cross flow model in multicomponent membrane gas separation is studied. Considering cross flow model, numerical methods such as Bogacki-Shampine method, Dormand-Prince method, Adams-Bashforth-Moulton method, numerical differentiation formulas, modified Rosenbrock formula of order 2, Trapezoidal rule with free interpolant an...

We outline a new class of robust and efficient methods for solving the Navier–Stokes equations with a Boussinesq model for buoyancy driven flow. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams–Bashforth method for error control, and a robust Krylov subspace solver for the spatially d...

Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams–Bashforth method for error control is assessed in this work. This combination is particularly well suited...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

In this paper we analyse the stability of weak discrete stationary shocks. The difference approximation is conservative, dissipative and k-th order accurate (k = 1 or k = 3). In Sections 1-3, following the previous results of D. Michelson we adapt the multistep methods RungeKutta and Adams-Bashforth to solve systems of conservation laws. In section 4 we analyse the stability of the numerical me...

In this paper, a fractional-order model for the spread of computer viruses with saturated treatment rate is presented. This model consists of three components: Susceptible, Infectious, and Recovered. The SIR epidemic model with saturated treatment rate is considered. The stability of the disease free and endemic equilibrium points are studied. The global stability of the disease free equilibriu...

In the literature, various types of parallel methods for integrating nonsti initial-value problems for rst-order ordinary di erential equation have been proposed. The greater part of them are based on an implicit multistage method in which the implicit relations are solved by the predictor–corrector (or xed point iteration) method. In the predictor–corrector approach the computation of the comp...

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...