Reciprocity is applied to the situation where numerical simulations are needed for a number of source locations but relatively a few receiver positions. By invoking source-receiver reciprocity, the number of simulations can be generally reduced to three times the number of receiver positions. The procedure is illustrated for a heterogeneous medium with both single-force and double-couple source...

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...

This paper considers the computational issue of the optimal stopping problem for the stochastic functional differential equation treated in [4]. The finite difference method developed by Barles and Souganidis [2] is used to obtain a numerical approximation for the viscosity solution of the infinite dimensional Hamilton-Jacobi-Bellman variational inequality (HJBVI) associated with the optimal st...

We study a superreplication problem of European options with gamma constraints, in mathematical finance. The initially unbounded control problem is set back to a problem involving a viscosity PDE solution with a set of bounded controls. Then a numerical approach is introduced, inconditionnally stable with respect to the mesh steps. A generalized finite difference scheme is used since basic fini...

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined...

Mimetic discretizations based on the support-operators methodology are derived for non-orthogonal locally refined quadrilateral meshes. The second-order convergence rate on non-smooth meshes is verified with numerical examples. 2004 Elsevier Inc. All rights reserved. PACS: 65N06; 65N22; 80A20

We do the numerical analysis and simulations for the time fractional radial diffusion equation used to describe the anomalous subdiffusive transport processes on the symmetric diffusive field. Based on rewriting the equation in a new form, we first present two kinds of implicit finite difference schemes for numerically solving the equation. Then we strictly establish the stability and convergen...

We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...

ABSTRACT The objective of this article is obtaining a mathematical model that describes the thermal problem in Grinding. A numerical solution of the equation of bi-dimensional heat diffusion is obtained. The numerical solution is made by the finite differences method, incorporating a scheme of fixed-point type Picard to solve the non-linealities introduced by the thermal properties of the mater...

A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational ...