Showing papers in "Applied Mathematics and Computation in 1981"

TL;DR: In this paper, two nonlinear transformations, the D-transformation to accelerate the convergence of infinite integrals and the d -transformation for infinite series, are presented, and the computational aspects of these transformations are described in detail.

TL;DR: The Chow-Yorke algorithm as discussed by the authors is a scheme for developing homotopy methods that are globally convergent with probability one, which has been successfully applied to a wide range of engineering problems, particularly those for which quasi-Newton and locally convergent iterative techniques are inadequate.

TL;DR: In this article, the Laguerre-transform method is extended to the full continuum, with Laurent expansions, bilateral Laplace transformation, and conformal mapping entering as crucial tools.

TL;DR: In this article, a new method for computing limit cycles that bifurcate from stationary solutions is proposed, which is very easy to implement, the method requiring the programming of the right-hand side only.

TL;DR: An integral transform which converts a real spatial (or temporal) function into a real frequency function is introduced in this paper, and the properties of this transform are investigated, and it is concluded that this transform is parallel to the Fourier transform and may be applied to all fields in which the FFT has been successfully applied.

TL;DR: In this article, the mean-square convergence and numerical stability of a collocation method for solving a class of Cauchy-singular integral equations was established, and stability was demonstrated by generalizing the approach of Atkinson for integral equations of the second kind.

TL;DR: An algorithm for spectral decomposition is presented which does not require knowledge of eigenvalues and eigenvectors, and a set of Eigenprojectors are defined which covers the entire spectrum of a matrix.

TL;DR: In this article, a learning approach to the two-person decentralized team problem with incomplete information and with a 2X2 payoff matrix is considered, and it is shown that there exists a proper choice of parameters of the learning algorithm that will ensure asymptotically an expected payoff as close to maximum payoff as desired.

TL;DR: A continuous frequency spectrum (W spectrum) is formed by a data sequence and the W transform of this spectrum is a continuous function which corresponds uniquely to the known data sequence.

TL;DR: In this article, a real representation for a periodic function by trigonometric series is described, and a generalized series expression of a function defined on a finite interval is formed and its properties are investigated.

TL;DR: The existence and structure of periodic orbits of the discrete delayed logistic equation x"n"=";1=rx"n(1-x"n)-"1) is studied in this paper.

TL;DR: The concept of k-sequential graphs was introduced in this article, where a graph G with |V(G)@? E(G)|=t is defined as a graph where there is a bijection such that for each edgee@?=xyin E (G) one has |?(e@?) = |@?(x)-@? (y)|.

TL;DR: In this paper, the deterministic limit of stochastic differential equations is investigated both as a verification of the theory and also for possible value as a deterministic technique, and the results show that it can be used both as verification of theory and as deterministic approach.

TL;DR: A complete differential-equation system has been developed for the local and nonlocal comparative static analysis of general parametrized economic systems @J(x, @a) = 0 as mentioned in this paper.

TL;DR: In this paper, the author's methods for solution of stochastic differential equations are shown to be applicable for nonlinear cases including polynomial, exponential, and trigonometric terms.

TL;DR: In this article, a method is developed for estimating the four parameters of stable Paretian distributions based on a procedure proposed by an earlier researcher but never developed, the method proves to be mathematically simple and easy to apply.

TL;DR: In this paper, an algorithm for the numerical solution of quite general two-parameter eigenvalue problems, whether singular or not, is described, based on the solution of suitable initial-value problems or ''shooting''.

TL;DR: The general theory of latent roots, latent vectors, and latent projectors is described and the relationships to eigenvalues, eigenvectors, and eigenprojectors of the companion form are given.

TL;DR: In this paper, an extension of Chartrand and Wall's theorem was obtained and, with it, a bound on the hamiltonian index h(G) of a connected graph G (other than a path) was determined.

TL;DR: The BIFOR2 as mentioned in this paper analyzes Hopf bifurcation points in ODEs by finding critical value(s) of a user-specified parameter v such that a stationary (equilibrium) solution x"*(v) loses linear stability by virtue of a complex conjugate pair of eigenvalues.

TL;DR: In this article, it was shown that previous work of Elder can be used to extend the version of invariant imbedding due to M. R. Scott to homogeneous (vector) differential systems having a singularity of the first kind.

TL;DR: In this article, the notion of coupled quasi-fixed points is introduced, and the main result shows their existence, and fixed point theorems of mixed monotone operators by iterative technique in a Banach space with the ordering relative to cone K.

TL;DR: In this article, the authors extend the monotone technique to a general class of nonlinear boundary value problems which includes the transport problem treated as a special case, and prove the existence of multiple solutions and point-wise bounds on solutions of such problems for both ordinary and partial differential equations.

TL;DR: In this article, the quasilinearization method was used to fit a standard two-sex population model, which involves nonlinear ordinary differential equations, to observational data.

TL;DR: In this article, an integrodifferential equation is derived which describes the motion of a phase transition of nonvanishing latent heat in a homogeneous body from a knowledge of only the Green's function and heat source, if present.

TL;DR: In this article, a Sylvester matrix for several polynomials has been defined, establishing the relative primeness and the greatest common divisor of polynomial matrices.

TL;DR: A comparison of Adomian's iterative method for stochastic differential equations and the Picard method of successive approximations is presented in this article, showing that the iterative procedure is more efficient and computationally useful even in the deterministic case.