Search results for "Boundary value problem"
showing 10 items of 551 documents
On the convergence of the finite element approximation of eigenfrequencies and eigenvectors to Maxwell's boundary value problem
1981
Interlaminar stresses in laminated composite beam-type structures under shear/bending
2000
A boundary integral model for composite laminates under out-of-plane shear/bending is presented. The formulation proposed allows one to determine the elastic response of generally stacked composite laminates having general shape of the cross section. The integral equations governing the ply behavior within the laminate are deduced starting from the reciprocity theorem for beam-type structures. The ply integral equations are obtained by employing the analytical expression of the fundamental solution of generalized plane strain anisotropic problems. The laminate model is completed by imposing the displacement and stress continuity along the interfaces and the external boundary conditions. The…
A non-local model of fractional heat conduction in rigid bodies
2011
In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent s…
Regularization and finite element approximation of the wave equation with Dirichlet boundary data
1990
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.
Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers.
2004
Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to Second Harmonic Generation (SHG) in the undepleted pump regime.
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
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.
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…
Building blocks for odd–even multigrid with applications to reduced systems
2001
Abstract Building blocks yielding an efficient implementation of the odd–even multigrid method for the Poisson problem in the reference domain (0,1) d , d=2,3, are described. Modifications needed to transform these techniques to solve reduced linear systems representing boundary value problems in arbitrary domains are given. A new way to define enriched coarser subspaces in the multilevel realization is proposed. Numerical examples demonstrating the efficiency of developed multigrid methods are included.