We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.

in this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. the given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. a set of temperature measurements at a single sensor location inside the heat conduction body is required. the result show that the proposed meth...

nowadays deep excavations are needed for construction of foundation of high rise buildings, providing space for parking and etc. in some cases deep excavations may be constructed in the vicinity of the subway tunnels and causes unpredicted extra displacements and internal forces in tunnel lining of tunnels which were not designed for them and consequently affect serviceability of tunnel. theref...

A numerical method of determining the wire sag in a multiwire proportional chamber used in RICH [1] by solving the second order differential equation which governs the wire stability has been presented. The three point Finite Difference Method (FDM) has generated a tridiagonal matrix equation relating the deflection of wire segments to the force acting on it. The precise estimates of electrosta...

Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being use...

For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...

where x = (x1, . . . , xd) ∈ IR , t > 0. HJ equations arise in many practical areas such as differential games, mathematical finance, image enhancement and front propagation. It is well known that solutions of (1) are Lipschitz continuous but derivatives can become discontinuous even if the initial data is smooth. There is a close relation between HJ equations and hyperbolic conservation laws. ...

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe s...