Ill PREFACE This Memorandum is part of RAND's continuing search for new ways of utilizing the modern digital computer. The authors present a method for numerically Integrating nonlinear partial differential integral equations, which occur In such fields as radiative transfer and mathematical biology. The method Is then specifically applied to solving a basic equation of transport In a spherical...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the Fock space structure. Using the state vector, the generating function is defined and the master equation of the system is transformed into the equation for the...

The linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear illposed integral equation of the first kind. An open issue in this technique is the one of determining the optimal scatterer profile from the visualization maps in an automatic manner. In the present paper this proble...

In this work we consider the solution of the linear systems arising from electromagentism applications by preconditioned Krylov subspace methods [3]. Simulation of electromagnetic wave propagation phenomena requires the numerical solution of Maxwell’s equations which it is often done by means of integral equation methods. The discretization of the integral equations with the boundary element me...

The boundary element method (BEM) for linear elasticity in its curent usage is based on the boundary integral equation for displacements. The stress field in the interior of the body is computed by differentiating the displacement field at the source point in the BEM formulation, via the strain field. However, at the boundary, this method gives rise to a hypersingular integral relation which be...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

In this work, we consider rational ordinary differential equations dy/dx = Q(x, y)/P (x, y), with Q(x, y) and P (x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for which a first integral can be expressed from two independent solutions of a second–order homogeneous linear differential equation. This first integral is, in general, given by a...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...