Almost all the difficulties that arise in the numerical solution of Maxwell’s equations are due to material interfaces. In case that their geometrical features are much smaller than a typical wave length, one would like to use small space steps with large time steps. The first time stepping method which combines a very low cost per time step with unconditional stability was the ADI-FDTD method ...

In this study, a new algorithm is introduced for the numerical solution of equal width (EW) equation. This created by using collocation finite element method based on decic B-spline functions space discretization EW equation and Crank-Nicolson time his The obtained results are compared with previous ones to see efficiency accuracy proposed method.

This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a practical (financial) perspective. This model turns to be Markovian in three dim...

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of di...

Based on the concept of alternating group and domain decomposition, we present a class of alternating group explicit-implicit method and an alternating group Crank-Nicolson method for solving convection-diffusion equation. Both of the two methods are effective in convection dominant cases. The concept of the construction of the methods is also be applied to 2D convection-diffusion equations. Nu...

|Reaction-diiusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diiusion system, of-! type. The two methods are a ...

Pressure correction schemes and the method of characteristics are combined to obtain numerical approximation procedures for incompressible Navier-Stokes ows on massive parallel computers. The projection step is carried out with a new more eecient parallel preconditioned conjugate gradient method and for the computation of the characteristics we use a fast local Crank-Nicholson solver for linear...

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the Navier-Stokes equations and a modification to the Crank-Nicholson method for the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth extrapolation and ...

Parallel multigrid methods are very prominent tools for solving huge systems of (non-)linear equations arising from the discretisation of PDEs, as for instance in Computational Fluid Dynamics (CFD). The superiority of multigrid methods in regard of numerical complexity mainly stands and falls with the smoothing algorithms (‘smoother’) used. Since the inherent highly recursive character of many ...

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, b...