Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this article, a model for solving the two-dimensional enhanced Boussinesq equations is presented, where the model equations are discretised in space using an unstructured finite element technique.
110 citations
TL;DR: An alternating-direction implicit (ADI) finite difference formulation for space-fractional diffusion equations in three space dimensions is presented and it is proved its unconditional stability and convergence rate provided that the fractional partial difference operators along x-,?y-,?z-directions commute.
110 citations
TL;DR: In this article, the discrete singular convolution (DSC) algorithm is used for the spatial discretization and the fourth-order Runge Kutta scheme for the time advancing.
110 citations
TL;DR: In this paper, a new technique is proposed to compute by Monte Carlo (or molecular dynamics) computer simulation the hydration free energy differences between dilute aqueous solutions of acetone and dimethyl amine.
Abstract: A new technique is proposed to compute by Monte Carlo (or molecular dynamics) computer simulation the hydration free energy differences. The method, called finite difference thermodynamic integration, is a combination of the thermodynamic integration and the perturbation method. It was compared with thermodynamic integration over two different paths and the perturbation method on computing the solvation free‐energy difference between the dilute aqueous solution of acetone and dimethyl amine. Finite difference thermodynamic integration was found to have the best convergence characteristics among the methods tested.
110 citations
TL;DR: In this article, the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two-point boundary-value problems by finite difference or finite element methods is considered.
Abstract: We consider the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two-point boundary-value problems by finite difference or finite element methods. An analysis of optimality of the mesh and optimal grading functions in various norms and seminorms for the interpolation problem leads to the formulation of an adaptive mesh redistribution algorithm for boundary-value problems in one dimension. Error estimates are given and numerical results presented to demonstrate the performance of the scheme and compare alternative redistribution criteria.
110 citations