Luis Casasús

The decomposition method for stiff systems of ordinary differential equations

In this paper, the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases, focusing our interest in stiff problems.

The decomposition method for ordinary differential equations with discontinuities

In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinary differential equations with discontinuities for both linear and nonlinear cases.

Approximate analytical solution of fourth order boundary value problems

Abstract In this paper, the decomposition method is applied to boundary-value problems of fourth order for ordinary differential equations.

An explicit finite differences scheme over hexagonal tessellation

Abstract We introduce a new numerical method inspired in the cellular automata methodology to study the transmission of waves in two-dimensional solids. The stability of the second-order method is investigated and compared with that of a classical finite differences method for both wave and elastic equations.

On the applicability of the Adomian method to initial value problems with discontinuities

Abstract In this paper we extend our results of L. Casasus, W. Al-Hayani [The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245–251] to initial value problems with several types of discontinuities, giving relevant examples of linear and nonlinear cases.

Efficiency on clusters of parallel simulation of sine-Gordon equation over hexagonal tessellation

Experiences in the parallel execution of a numerical method to simulate the sine-Gordon equation over two different clusters are presented in this paper. The nonlinear sine-Gordon equation has been discretized in a finite differences method based on hexagonal tesselation, and then parallelized using MPI for parallel execution on three workstation clusters, a Pentium III PC based cluster using Gigabit Ethernet and Myrinet as interconnection networks, an Itanium2 based HP RX2600 cluster with Gigabit Ethernet, and a Prescott based PC cluster. Efficiency measurements over these clusters are also studied and compared.

Parallel Simulation of Non-linear Phenomena with Cellular Automata

This paper presents a new approach to the problem of simulating wave propagation in elastic solids, using Cellular Automata. The main objective of this work is to develop a cellular automaton model which allows to understand several complex or non-linear phenomena that occur in the propagation of stress waves. These phenomena, such as soliton propagation, viscoelasticity, discontinuities, fracture mechanics and many others, are often hardly expressed by means of differential equations, or, if they do, it is very difficult to solve the final equations analytically. By the use of CA, where a microscopical description of the behaviour of each element is made, it is intended to prove that complex phenomena such as plasticity, energy losses and so on can be worthily simulated. This kind of description makes easier the experimentation with many different systems, since the number of characteristic parameters is small.