Contents Preface Introduction xv 1 1.1 A one-dimensional model problem 2 1.2 A two-dimensional example of heat propagation in a heterogeneous material 3 1.3 Examples of irregular domains and free boundary problems 5 1.4 The scope of the monograph and the methodology 5 1.4.1 Jump conditions 7 1.4.2 The choice of grids 7 1.5 A minireview of some popular finite difference methods for interface pro...

A (v, k, λ) difference family ((v, k, λ)-DF in short) over an abelian group G of order v is a collection F = {Bi | i ∈ I} of k-subsets of G, called base blocks, such that each nonzero element of G can be represented in precisely λ ways as a difference of two elements lying in some base blocks in F . A disjoint (v, k, λ)-DF is a difference family with disjoint blocks. In this paper, it is proved...

In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...

This article presents a Monte Carlo methodology for solving the stochastic optimal timber harvest problem modeled as a recurrent American call option. A detailed description of the proposed methodology is given, and the Monte Carlo technique is contrasted with finite difference methods typically used to find solutions of the optimal harvest problem with stochastic prices. The use of the methodo...

A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct and they determine the different scales in the solution to this problem. A Shishkin piecewise–uniform mesh is constructed, which is used, in conjunct...

Three-dimensional model is established with finite difference method to simulate construction process based on design and construction plans of existing overpass pile foundation adjacent to certain large-section railway tunnel in Chengdu, China. Ground, isolation pile, main bridge pier and ramp pile near the tunnel are taken as research object, and surface settlement amount, displacement change...

In this article we introduce the multi-domain hybrid Spectral-WENO method aimed at the discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the non-oscillatory properties of the high order weighted essentially non-oscillatory (WENO) finite difference schemes with the high computational efficiency and accuracy of spectral methods. Built in a multi-domain framewo...