Search results for "Modeling and simulation"
showing 10 items of 1561 documents
DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
1998
Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010
Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem
2015
We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.
ON SOLVABILITY OF THE DAMPED FUČÍK TYPE PROBLEM WITH INTEGRAL CONDITION
2014
The solvability results are established for the boundary value problem with a damping term , x(0) = 0, where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0
Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators
2017
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…
Nonlocal Third Order Boundary Value Problems with Solutions that Change Sign
2014
We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.
A branch-and-cut algorithm for the Orienteering Arc Routing Problem
2016
[EN] In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP),in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route.In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds…
Matheuristics for the irregular bin packing problem with free rotations
2017
[EN] We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientation…
Bidirectional labeling in column-generation algorithms for pickup-and-delivery problems
2018
Abstract For the exact solution of many types of vehicle-routing problems, column-generation based algorithms have become predominant. The column-generation subproblems are then variants of the shortest-path problem with resource constraints which can be solved well with dynamic-programming labeling algorithms. For vehicle-routing problems with a pickup-and-delivery structure, the strongest known dominance between two labels requires the delivery triangle inequality (DTI) for reduced costs to hold. When the direction of labeling is altered from forward labeling to backward labeling, the DTI requirement becomes the pickup triangle inequality (PTI). DTI and PTI cannot be guaranteed at the sam…
Advanced Greedy Randomized Adaptive Search Procedure for the Obnoxious p-Median problem
2016
Abstract The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP -hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the Greedy Randomized Adaptive Search Procedure, GRASP, methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avo…
On Mathematical Modelling of Metals Distribution in Peat Layers
2014
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodica…