This chapter presents some applications of nonstandard finite difference methods to general nonlinear heat transfer problems. Nonlinearity in heat transfer problems arises when i. Some properties in the problem are temperature dependent ii. Boundary conditions are described by nonlinear functions iii. The interface energy equation in phase change problems is nonlinear. Free convection and surfa...

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...

With the rise in popularity of compatible finite element, finite difference and finite volume discretizations for the time domain eddy current equations, there has been a corresponding need for fast solvers of the resulting linear algebraic systems. However, the traits that make compatible discretizations a preferred choice for the Maxwell’s equations also render these linear systems essentiall...

plains why it is expedient to use two distinct and dual discretization grids, it shows how they must be staggered In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminatto achieve optimal performance and proposes a technique ing the similarity between the discretization strategies adopted by for the construction of high o...

A new resistance simulator for extraction of the parasitic parameters from VLSI layout is presented. The calculation of resistor network is based on the boundary element method (BEM). The computational results indicate that the BEM has an advantage over the finite difference method (FDM) and the finite element method (FEM). Since only discretized equations on the boundary of solved domain need ...

Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an impl...

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...

The magnetohydodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system,...

Solving the Saint-Venant equations by numerical methods like finite element and finite difference methods yields an unstable solution for a fairly large open channel. Multiple Knot B-Spline Wavelets (MKBSW) are in the class of semi-orthogonal wavelets that have compact support. Hence, these basis functions are suitable for solving the Saint-Venant equations. However, solving the Saint-Venant eq...

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...