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Showing papers in "Journal of Computational and Applied Mathematics in 1978"


Journal ArticleDOI
TL;DR: In this article, a branch of solutions of a system of nonlinear equations dependent upon a scalar parameter is followed through a turning point and an efficient method, with second order convergence, for finding the turning point is described.

119 citations


Journal ArticleDOI
TL;DR: In this article, a continued fraction expansion in two variables is described and shown to correspond to a double power series, which is a natural generalization of the S-fraction and can be truncated to form a sequence of rational approximants.

48 citations


Journal ArticleDOI
TL;DR: In this article, the Hermite spline interpolant (HSI) of degree 2q −1 was used to approximate the function f e C 1 [a, b] by convex HSI.

30 citations


Journal ArticleDOI
TL;DR: Two efficient third-and fourth-order processes for solving the initial value problem for ordinary differential equations are studied and both are A-stable and so recommended for stiff systems.

29 citations


Journal ArticleDOI
TL;DR: In this article, the numerical calculation of the [ n + 1] 2 nonnegative abscissas and corresponding weights for the n-point Gauss-Legendre integration rule was studied.

26 citations



Journal ArticleDOI
TL;DR: In this paper, a bibliography on interval mathematics appeared in this Journal and the present contribution will update this bibliography, including corrections of misprints and bibliographical data for those papers being notified in the last issue of the bibliography as "to appear" ("erscheint demn/ichst').

13 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of carrying out an asymptotic analysis for the phenomenon of bifurcation which occurs at critical values of an axial force applied to an elastic column.

8 citations


Journal ArticleDOI
TL;DR: In this article, the Lanczos procedure of orthogonalization is used to calculate the elements of a N-dimensional Jacobi matrix and coefficients of the three-term recurrence relation of a system of Orthogonal polynomials {Pm(x), m = 0, 1, 2, −, N} in terms of the moments of its associated weight function.

8 citations


Journal ArticleDOI
TL;DR: In this paper, the choice of the value of θ in the θ-method is discussed and the number of iterations in the solution of algebraic equations with matrix of the form M + (1 − θ) τ K with M mass matrix, K stiffness matrix, has been studied, both for linear and for nonlinear problems.

7 citations


Journal ArticleDOI
TL;DR: A new exact algorithm based on the interdependence between the travelling salesman problem and the seriation problem is presented, which can handle larger problems than any of the existing exact algorithms.

Journal ArticleDOI
TL;DR: In this article, an easily programmed method is presented for solving N linear equations in N unknowns exactly for the rational answers, given that all coefficients and constants appearing in the equations are rational numbers.

Journal ArticleDOI
TL;DR: The generalization of a continued fraction in the sense of the Jacobi-Perron algorithm (called an n-fraction ) is considered and a new one is derived and the algorithms are compared with respect to the number of operations required and the time to executed.

Journal ArticleDOI
TL;DR: In this paper, an analysis for the expansion of a gamma function ratio discussed by Stieltjes and others is given, affording lower and upper bounds, but lacking a rigorous proof.

Journal ArticleDOI
TL;DR: In this paper, the problem of finding the solution of a two-point boundary value for a 6-order nonlinear ordinary differential equation and three boundary conditions at each of a finite interval is reduced to that of finding a solution of the boundary value.

Journal ArticleDOI
TL;DR: Computer experience with Muller's method indicates that it is very efficient algorithm for computing real, complex, and multiple zeros of arbitrary functions and its efficiency is compared to that of a good bracketing algorithm.

Journal ArticleDOI
TL;DR: In this article, difference schemes of sixth order with off-step points have been obtained and applied to the second order differential equation, with and without mixed boundary conditions, and the results obtained by these methods have been compared with those obtained by using h 4 -extrapolation of the Numerov method.

Journal ArticleDOI
TL;DR: Several step-by-step methods for the computer solution systems of coupled second-order ordinary differential equations, are examined from the point of view of efficiency “time-wise" and “storage-wise”.

Journal ArticleDOI
TL;DR: In this article, the problem of determining the roots of simple algebrac equations by constructing polynomial equations that have the same roots is dealt with, and the problem is solved.

Journal ArticleDOI
TL;DR: In this article, a cumulative sum test for detecting change in the transfer function of open loop stochastic systems is proposed based on the logarithmic transformation of the evolutionary gain-spectra estimate.

Journal ArticleDOI
TL;DR: Three Ritz-Galerkin procedures with Hermite bicubic, bicubs spline and linear triangular elements for approximating the solution of self-adjoint elliptic partial differential equations and a collocation method for general linear elliptic equations defined on general two dimensional domains with mixed boundary conditions are considered.

Journal ArticleDOI
TL;DR: In this paper, the authors adapted the Berry-Esseen theorem concerning convergence to a stable law for a sum of independent identically distributed (i.i.d.) random variables to the case of a compound Poisson process, considered in the collective risk theory.

Journal ArticleDOI
TL;DR: In this article, a complex Laplace transform function was inverted by three numerical methods and compared to the small time and large time approximation curves, and the best choice of an inversion method was made, since one method gave excellent results, at both small and large times and moved smoothly from one curve to the other.

Journal ArticleDOI
TL;DR: This paper derived analytical expressions for the eigenvalue bounds of matrices arising when using a fast method for separable finite difference equations for the numerical solution of the first three boundary value problems for the two-dimensional self-adjoint second order elliptic partial differential equation in a rectangle.

Journal ArticleDOI
TL;DR: In this paper, a design procedure for pole allocation for single-input single-output (SISO) systems with time delays is presented, which allows a straightforward calculation of the feedback matrix to attain prescribed closed-loop pole positions.

Journal ArticleDOI
TL;DR: In this paper, a perturbation technique for nearly linear oscillatory systems is developed and a set of second order averaged equations is obtained, where the standard form treated is dx dt = F (x, t ; ϵ), |ϵ| ⪡ 1, and a well known example is considered in detail so as to show how the asymptotic approximations of other methods can be obtained.

Journal ArticleDOI
TL;DR: Hopscotch methods for solving time dependent partial differential equations are derived using a locally-one-dimensional splitting instead of the standard alternating direction splitting as discussed by the authors, and their possible flexibility in certain situations is discussed.

Journal ArticleDOI
TL;DR: In this article, it was shown that one-parameter methods for scattering amplitudes are equivalent to Aitken's Δ 2 transformation applied to successive elements of a Born sequence.

Journal ArticleDOI
TL;DR: In this paper, the authors considered whether a linear combination of three A-acceptable Pade approximations to the exponential function remains A-approachable when it is exponentially fitted to two distinct negative points.

Journal ArticleDOI
TL;DR: In this paper, a new, computer approach to the study of the interactions of particles with differing masses is applied to study of planetary type evolution, which contains an inherent self-reorganization property in which particles self-stratify in accordance with their masses.