Showing papers in "Applied Mathematics and Computation in 1975"

TL;DR: A comparison of several invariant imbedding algorithms for the numerical solution of two-point boundary-value problems is presented, including the Scott algorithm, the Kagiwada-Kalaba algorithms, the addition formulas, and the sweep method.

TL;DR: In this article, the problem of remotely sensing the optical properties of scattering particulates from the variations in either the angular or the spectral characteristics, or both, of the radiation they transmit or scatter, is a problem of fundamental importance in monitoring of environmental particulate pollution.

TL;DR: In this article, the critical length (escape time) associated with a solution of a matrix Riccati equation is shown to be bounded in terms of a known value of the solution at any point.

TL;DR: In this article, a novel general direct iteration algorithm for the evaluation of branching points of nonlinear boundary-value problems is suggested, which is tailored to problems of diffusion and heat conduction accompanied by a chemical reaction.

TL;DR: In this paper, the Riccati transformations are derived from mathematical arguments rather than physical ones for a general class of two-point boundary value problems, and the equivalence of solving a family of 2PV problems and determining the existence of two transformations on the set of solutions is established.

TL;DR: A new derivation of the Nordsieck form of the Adams methods reveals that codes based on this form have changed order incorrectly and shows how to do it properly.

TL;DR: In this paper, the authors investigated the relation between linear stochastic estimation theory and radioactive transfer in the atmosphere and showed that the two theories are virtually equivalent and that basic functions in one may be meaningfully interpreted in the context of the other.

TL;DR: In this paper, an iterative scheme for solving the radiative transfer equation in a scattering, absorbing and emitting slab with specularly reflecting boundary is presented, and the sequence of iterations from the recursion formula converges uniformly to a unique positive solution of the problem, so that this method also gives an existence and uniqueness theorem.

TL;DR: In this article, an initial value method for the integral equation of the column is presented for determining the buckling load of columns, which is reduced to a set of ordinary differential equations with prescribed initial conditions to find the Fredholm resolvent.

TL;DR: In this article, a new technique is presented for the calculation of the eigenvalues and eigenfunctions of integral operators where the kernel is an entire function of the Eigenvalue parameter.

TL;DR: In this article, a transonic relaxation program was used to analyze the inviscid flow through a cascade without splitters in order to verify the results of a previous experimental investigation, and the analysis showed that viscous effects play a large part in the development of the flow field in the transonic flow regime.

TL;DR: In this article, the same authors derived the same Cauchy system via the Wiener-Hopt procedure, and showed that the solution of a system of integral equations can be approximated by the same solution of the Cauche system.

TL;DR: An overview of the complete microeconometric model of the health care system of the United States is presented, and the relationships used for the hospital sector are summarized.

TL;DR: In this article, the authors compared the relative efficiencies of the invariant imbedding method with the traditional solution techniques of successive approximations (Picard method), linear algebraic equations, and Sokolov's method of averaging functional corrections in solving numerically two representatives of a class of Fredholm integral equations.

TL;DR: In this paper, a set of functional relations analogous to the addition formulas for the trigonometric functions is developed for a class of inhomogeneous linear two-point boundary value problems, which are implicit ones connecting values of the solutions at three points.

TL;DR: In this article, it was shown that the method introduced by Kalaba and Scott for solving nonlinear characteristic value problems for integral operators is equivalent to a nonlinear feature value problem for a matrix.

TL;DR: The optimal constant gain output feedback control of linear time-invariant discrete systems with respect to an averaged performance criterion is discussed and a method for computing the constant optimal feedback gain is presented.

TL;DR: The shape of a wire confined to the surface of a sphere with its ends tangent to two given circles of lattitude and otherwise free, in its most relaxed state, is found by solving a variational problem to be the solution of a fourth order nonlinear two point boundary value problem as mentioned in this paper.

TL;DR: In this paper, the eigenvalues of the Sturm-Liouville problem were estimated by making linear approximations of q(x) over subintervals of [0, 1] when q (x) has a bounded second derivative.

TL;DR: In this paper, a technique is developed to estimate an unknown curve joining two points in a 3D Euclidean space, where the set (x,y(x)) lies on the projection of the intersection of two surfaces and the function y is determined by least square curve fitting on a Latin square of experimental values.

TL;DR: In this article, the use of invariant imbedding in the solution of a variety of problems has been increasing, and application of this method to problems in heat conduction and radiation is demonstrated.