In this paper, we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle. Some results on the composite Laguerre-Legendre interpolation, which is a set of piecewise mixed interpolations coupled with domain decomposition, are established. As examples of applications, the composite pseudospectral schemes are provided for two model problems. The co...

This paper deals with the first step in the modeling of newe stimulation: the calculation of the potential field in a 3D volume conductor model of the nerve. surroundings and electrodes. Because of its time efficiency, a multigrid method was used to calculate the field. Compared to a Gauss-Seidel relaxation (overrelaxation factor = 1.7). a calculation time reduction of a factor 20 was obtained,

Numerical solutions are presented for steady two-dimensional motion within a circular cylinder generated by uid injecting radially over one small arc and ejecting radially over another arc. These solutions are based on a mixed nite-diierence pseudospectral method. Previous calculations were able to obtain convergent results only for a range of Reynolds numbers from R = 0 to R = 20. The main obj...

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...

As a first application of the new adaptive mesh functionality pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to threshold collapse. We consider six different one-parameter families Brill wave initial data; two centered and four off-centered families. Of these latter have not been treated before. Within each family, tune parameter tow...

In adirect collocation pseudospectralmethod, a continuous-time optimal control problem is transcribed to afinitedimensional nonlinear programming problem. Solving this nonlinear programming problem as efficiently as possible requires that sparsity at both the firstand second-derivative levels be exploited. In this paper, a computationally efficient method is developed for computing the first an...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...