Related papers: An Integral Equation Method for Linear Two-Point B…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the…
One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
On the basis of generalization of upper and lower solution method to the singular two point boundary value problems, the existence theorem of solutions for the system, which models a process of magnetic insulation in plasma is proved.
A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in three dimensions is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a…
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
Several numerical differential equation solvers have been employed effectively over the years as an alternative to analytical solvers to quickly and conveniently solve differential equations. One category of these is boundary value solvers,…
In this paper the isogeometric Nystr\"om method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only…
In this paper we propose and analyze a class of simple Nystr\"om discretizations of the hypersingular integral equation for the Helmholtz problem on domains of the plane with smooth parametrizable boundary. The method depends on a parameter…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.