This paper proposes the use of the Spectral method to simulate diffusive moisture transfer through porous materials, which can be strongly nonlinear and can significantly affect sensible and latent heat transfer. An alternative way for computing solutions by considering a separated representation is presented, which can be applied to both linear and nonlinear diffusive problems, considering hig...

In the present investigation heat transfer character due to viscous dissipation and magnetic field applied to unsteady boundary layer fluid flow past a stretching sheet is investigated. The equations governing the unsteady boundary layer fluid flow are constructed and non-dimensionalized. The non-dimensional equations are discretized using implicit finite difference method of Crank-Nicolson typ...

In this note, we formulate a theorem giving bounds on the powers of linear operators, in a general Banach space setting. The relevance of the theorem is illustrated by applying it to the Crank-Nicholson method for the numerical solution of the heat equation. This application yields a stability estimate in the maximum norm which amounts to an improvement over a well-known result of Serdjukova [l...

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger’s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton’s explicit group iterative methods for a general Burger’s equation. The propo...

This paper adresses the construction and study of a Crank-Nicolson-type discretization of the two-dimensional linear Schrödinger equation in a bounded domain Ω with artificial boundary conditions set on the arbitrarily shaped boundary of Ω. These conditions present the features of being differential in space and nonlocal in time since their definition involves some time fractional operators. Af...

0021-9991/$ see front matter 2008 Elsevier Inc doi:10.1016/j.jcp.2008.06.032 * Corresponding author. Tel.: +1 609 243 2635; fa E-mail address: [email protected] (S.C. Jardin). In solving the 1D (flux surface averaged) transport equations for the temperatures, magnetic fields, and densities in the ‘‘evolving equilibrium” description of a tokamak [1], one increasingly encounters highly nonlinear th...

We construct and analyze a least-squares procedure for approximately solving the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Í2 in Ä , with homogeneous Dirichlet boundary conditions. The method is based on Crank-Nicolson time differencing. To approximately solve the resulting system of boundary value problems at each time step, a least-...

Blood flow is modeled as non-Newtonian micropolar fluid. The non-linear governing equations of continuum and momentum in the cylindrical coordinate are being discretized using a finite difference approach and have been solved iteratively ,through Crank-Nicolson method. The blood velocity distribution, volumetric flow rate and Resistance to blood flow at the stenosis throat are computed for vari...

This article provides a practical overview of numerical solutions to the heat equation using the finite difference method. The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem involving the one-dimensional heat equation. Complete, working Matlab codes for each scheme are presented. The result...