Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equation...

In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind fini...

Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...

Numerical Simulation of three dimensional wave equation is conducted in a cubic domain which contains two parts, part A and part B. Part A of the domain is a I -shaped empty channel, containing air, and part B, containing a solid medium, is the difference between the whole cubic domain and part A. A Dirichlet type boundary condition is specified at the inlet boundary. At all other boundaries of...

Stabilized explicit-implicit domain decomposition is a group of methods for solving time-dependent partial difference equations of the parabolic type on parallel computers. They are efficient, stable, and highly parallel, but suffer from a restriction that the interface boundaries must not intersect inside the domain. Various techniques have been proposed to handle this restriction. In this pap...

in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...

The modeling of physical systems often leads to partial differential equations (PDEs). Usually, the equations or the domain where the equations are posed are so complicated that the analytic solution cannot be found. Thus, the equations must be solved using numerical methods. In order to do this, the PDEs are first discretized using the finite element method (FEM) or the finite difference metho...

The application of fourth-order finite difference discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined further. In the bulk of the diffusion space, a central 5-point scheme is used, and 6-point asymmetric schemes are used at the edges. In this paper, four Runge-Kutta schemes have been used for ...

We present a domain decomposition method for computing finite difference solutions to the Poisson equation with infinite domain boundary conditions. Our method is a finite difference analogue of Anderson’s Method of Local Corrections. The solution is computed in three steps. First, fine-grid solutions are computed in parallel using infinite domain boundary conditions on each subdomain. Second, ...