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SUMMARY In this work, an explicit family of time marching procedures with adaptive dissipation control is introduced. The proposed technique is conditionally stable, second-order accurate, and has controllable algorithm dissipation, which adapts according to the properties of the governing system of equations. Thus, spurious modes can be more effectively dissipated and accuracy is improved. Because this is an explicit time integration technique, the new family is quite efficient, requiring no system of equations to be dealt with at each time step. Moreover, the technique is simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed method, as well as its potentialities. Copyright © 2014 John Wiley & Sons, Ltd.

An investigation of the impact of the temporal discretization on the marching-on-in-time solution of integral equations is presented. Numerical results that quantify the efficiency–accuracy tradeoff for causal piecewise polynomial and band-limited interpolatory functions are presented. It is observed that the former is more efficient for low to moderate accuracy levels, and the latter achieves higher, but extrapolation-limited, accuracy levels. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1343–1348, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25960

A time-marching formulation is derived from the space–time integrated least squares (STILS) method for solving a pure hyperbolic convection equation and is numerically compared to various known methods. Copyright © 2004 John Wiley & Sons, Ltd.

In this paper, we present a method for obtaining stable time marching equations of distributed multiport networks with nonlinear loads. This method allows to highly decrease the number of frequency samples required by other stable TM methods. Stability is analyzed and ensured in the Z‐domain.

In this letter, a high order accurate FDTD method is proposed, in which a fourth-order accurate staggered backward differentiation integrator is used for time marching and a new finite difference scheme named the optimal central finite difference scheme is used for spatial discretization. The analysis shows that the numerical dispersion of the new method can be reduced to some extent in comparison with that of the former fourth-order accurate FDTD method while no extra computation cost is involved. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1802–1804, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22605

A time marching integral equation method has been proposed here which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock wave motions. Firstly, a model problem–one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for two dimensional unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.

A general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented. This algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities. In many cases it presents a computationally advantageous form over conventional procedures—this is particularly so when compared with the Newmark algorighm and its variants.

Presentation d'un algorithme aux elements finis pour les equations determinant la dynamique de la convection a double diffusion. Exemples d'applications numeriques et comparaison avec des resultats experimentaux. Discussion des extensions possibles a d'autres problemes