Showing papers in "Journal of Computational and Applied Mathematics in 1977"

TL;DR: Hopscotch, a fast finite difference technique, is used to solve parabolic and elliptic equations in two space dimensions with a mixed derivative as discussed by the authors, and the method is compared numerically with existing alternating direction implicit (A.D.I.) and locally one dimensional (L.O.D.) methods for simple problems.

TL;DR: In this paper, a Lagrange interpolation formula was proposed for the simultaneous determination of the zeros of real polynomials, which can be viewed as an improvement on that of Nourein.

TL;DR: In this paper, a method is presented for fitting a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independent variables.

TL;DR: In this article, a class of explicit three-step Runge-Kutta methods is discussed for the numerical solution of initial value problems for systems of ordinary differential equations, which originate from parabolic partial differential equations by applying the method of lines.

TL;DR: In this paper, alternating direction implicit (A.D.I) methods are derived for solving fourth order parabolic equations with variable coefficients in one, two, and three space dimensions.

TL;DR: In this paper, the numerical integration of functions with poles near the interval of integration is studied, and a method is given for modifying known quadrature rules to obtain rules which are exact for certain classes of rational functions.

TL;DR: In this article, problem-dependent upper and lower bounds are given for the stepsize taken by long Taylor series methods for solving initial value problems in ordinary differential equations. But these bounds depend on the series length, radius of convergence, order, and location of the primary singularities.

TL;DR: In this paper, a method to calculate the asymptotic eigenvalue density (asymptotical density of zeros) of Jacobi matrices (orthogonal polynomials) in terms of its moments is presented.

TL;DR: In this paper, a Gauss-Seidel iterative algorithm is proposed to solve a set of nonlinear equations with the assumption that a solution exists, and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known.

TL;DR: This paper develops a theorem in n-dimensional Laplace transformation and applies this theorem to compute Laplace transform pairs inn-dimensions, as it is not easy to tackle this problem otherwise in a neat form.

TL;DR: A model for radiation-treatment planning is obtained that is discretized and so reduced to a practical form, and an example demonstrates the application of the system to a kidney tumour.

TL;DR: In this article, the finite Fourier transform of a B-spline is computed for a function given at a discrete set of arbitrary points, and the coefficients of the function can be computed at arbitrary points.

TL;DR: In this article, Borel models are applied to summing series for the moments of the sample standard deviation, Student's t, and the skewness statistic/b 1. Sampling is from an exponential density.

TL;DR: In this paper, a new type of modeling of physical phenomena is developed for systems of particles of differing masses, where initial value problems must be solved by means of modern, high speed digital computation.

TL;DR: A new algorithm is described in the paper for calculating continued fractions and the conditions are given under which this algorithm is faster than the hitherto fastest algorithm for handling this problem.

TL;DR: In the classical risk model, an insurer pays claim costs at the instants of their occurrence and receives premiums in a continuous linear way as discussed by the authors, and it is known that, under specified assumptions, the probability of non-ruin in the finite interval (o, t) equals 1t^q^=^1^c^t^@!

TL;DR: In this paper, the authors proposed a method of computing scattering amplitudes and cross-sections, which is by far more efficient but not much more cumbersome than the Born approximation, and applies to the cases of medium strong couplings in high as well as low energy region.

TL;DR: In this article, the authors used a combination of multiple shooting and range extension in such a way that the advantages of both methods are maintained while the effects of their disadvantages are reduced considerably.

TL;DR: In this paper, an iterative method for solving the matrix equation XA + AY = F is presented, and an algorithm with acceleration parameters is provided, where the acceleration parameters are chosen by the authors.

TL;DR: In this paper, a nonlinear method for the acceleration of multidimensional sequences {S"k} is described by generalising a connection between the @e-algorithm and Pade approximants.

TL;DR: In this paper, necessary and sufficient conditions for the existence of linear independent periodic zero-elements of period [email protected], m @? @?, of Hill's differential operator D^2 + Q, with @w being the minimal period of the function Q, were given.

TL;DR: In this paper, a linear multistep scheme of order four is presented for numerical solution of ODEs having oscillatory solutions, where the necessary starting values for the integration scheme are generated by an adaptation of the variable order Gragg-Bulirsch-Stoer algorithm.

TL;DR: In this article, rotationally covariant approximants were used to reproduce the locus of singularities and exponents of functions with singularities of the form [x - x"S (y)]^-^@c, where x'S(y) is linear in y.

TL;DR: In this article, a family of examples is constructed to show that if B is the k x n matrix (I"k|Z)U, where U is an n x n orthogonal matrix, then the eigenvalues of U do not affect the value of divergence D"B in the space of reduced dimension.

TL;DR: In this article, a modification of Greenstadt's method is proposed, where bounds on the eigenvalues of G ∗ may be imposed such that G ∆ has a spectral condition number identical to G when G is well-conditioned but indefinite.

TL;DR: In this paper, an easy-to-use three-dimensional plotting program is presented, written in ANSI FORTRAN IV, and is portable and can be used in any computer.

TL;DR: In this paper, first and second order Runge-Kutta formulas for the integration of systems of differential equations are discussed, whose parameters are square matrices with component-dependent values.

TL;DR: This is the first part of a bibliography on computational probability, which lists over five hundred reference to published papers, technical reports and theses which deal with algorithmic solutions to probability problems or which contain useful information on the computational aspects of such problems.

TL;DR: In this article, a scheme for the construction of a visually smooth and fair space curve passing through a prescribed sequence of irregularly spaced and non-coplanar points is proposed.