Nonuniform grids

We propose a new monotone finite-difference scheme for the second-order local approximation on a nonuniform grid that approximates the Dirichlet initial boundary value problem (IBVP) for the quasi-linear convection-diffusion equation with unbounded nonlinearity, namely, for the Gamma equation obtained by transformation of the nonlinear Black-Scholes equation into a quasilinear parabolic equation. Using the difference maximum principle, a two-sided estimate and an a priori estimate in the c-norm are obtained for the solution of the difference schemes that approximate this equation.

6p chauchaungayxua2 07-01-2020 29 1   Download

In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain.

10p danhdanh27 07-01-2019 20 1   Download

The goal of autonomic computing is the reduction of complexity in the management of large computing systems. The evolution of computing systems faces a continuous growth in the number of degrees of freedom the system must manage in order to be efficient. Two major factors contribute to the increase in the number of degrees of freedom: Historically, computing elements, such as CPU, memory, disks, network and so on, have nonuniform advancement. The disparity between the capabilities/speeds of various elements opens up a number of different strategies for a task depending upon the environment..

11p huggoo 20-08-2010 78 6   Download