We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H−1 norm. We prove convergence of a discrete optimal control problem based on a monotone finite differenc...

Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient. © 2009 IMACS. Published by Elsevier...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...

We study Soret-Dufour and radiation effects on unsteady viscous incompressible MHD flow along semi infinite inclined permeable moving plate with variable temperature and mass diffusion embedded in a porous medium numerically, by taking into account the effect of viscous dissipation. The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference me...

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximu...

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

: : In this paper, we present a new approach to resolve linear weakly-singular partial integro-differential equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential equations into an partial differential equation. After that the fourth order compact finite difference scheme and collocation method is presented to obtain system o...

Wavelet analysis provides information on the energy present at various scales and locations throughout a computational domain. This information is precisely the information that is needed to define the appropriate gridpoint densities and the appropriate numerical order to resolve the physics at hand in the computationally most efficient manner. Here a two-dimensional version of the numerical me...

An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order...

In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both d...