Group explicit methods for hyperbolic equations

AbstractHere the strategy of the group explicit (GE) methods is applied to the numerical solution of hyperbolic partial differential equations. Theoretical aspects of the stability, consistency, convergence and truncation errors of this new class of methods are presented with supporting numerical evidence

Group explicit methods for the numerical solution of the wave equation

AbstractThe applicability of the group explicit (GE) methods to the numerical solution of hyperbolic partial differential equations of second-order is discussed in this paper following closely many of the ideas presented in an earlier related paper

The D'Yakonov fully explicit variant of the iterative decomposition method

AbstractIn this paper, a new iterative alternating decomposition (IADE) scheme of (4,2) order of accuracy is developed to solve the one-dimensional parabolic problem. It is based on the two-stage fractional splitting strategy suggested by D'Yakonov and found to be generally more accurate than the recently developed (2,2) accurate alternating group explicit (AGE) method of Peaceman-Rachford variant. As the method is fully explicit, its feature can be fully utilized for parallelization by means of a domain decomposition strategy

Fourth order approximation with complexity reduction approach for the solution of time domain Maxwell equations in free space

Propagation of electromagnetic fields from an antenna in a free space can always be modelled by time domain Maxwell equations. The equations have been used since their creation by Maxwell. Finite difference time domain (FDTD) method has been used since 1966 to model the propagation of electromagnetic fields. Previously, we have developed a new version of FDTD method called HSLO-FDTD. The method has shown to solve a 1D free space wave propagation problem 67% faster than the conventional FDTD. The parallel version of the method is then extended to solve 2D free space wave propagation problem. It is found that the method is 85.2% faster than the parallel FDTD method. In this paper, we further extend the method using the combination of fourth order approximation with the complexity reduction approach. The method shows to be faster than the conventional FDTD to simulate the 2D free space wave propagation problem

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered

Numerical methods for solving hyperbolic and parabolic partial differential equations

SIGLEAvailable from British Library Document Supply Centre- DSC:D68018/86 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Group explicit methods for hyperbolic equations

AbstractHere the strategy of the group explicit (GE) methods is applied to the numerical solution of hyperbolic partial differential equations. Theoretical aspects of the stability, consistency, convergence and truncation errors of this new class of methods are presented with supporting numerical evidence