Showing papers in "Journal of Computational and Applied Mathematics in 1980"

TL;DR: In this article, a family of embedded Runge-Kutta formulae RK5 (4) are derived from these and a small principal truncation term in the fifth order and extended regions of absolute stability.

TL;DR: In this article, a subroutine for automatic numerical integration is presented, which is developed by changing the basic rule used in an algorithm of P. van Dooren and L. de Ridder.

TL;DR: In this article, a branched continued fraction (BCF) is defined and some properties of BCF are shown, which corresponds to the double power series, and one theorem of Van Vleck is transformed for the case of double-power series and BCF.

TL;DR: In this paper, methods of order 2, and 4 are developed for the continuous approximation of the solution of a two-point boundary value problem involving a fourth order linear differential equation via quintic and sextic spline functions.

TL;DR: In this paper, a method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed-loop system matrix is proposed based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form.

TL;DR: In this paper, the Viskovatoff algorithm is generalized to cover the computation of continued fractions whose successive convergents form the Pade approximants of a descending staircase or diagonal.

TL;DR: In this paper, an Algol 60 procedure is described which will estimate the first, second or third order derivative of a function at a point x 0, using polynomial interpolation to values of f(x) at points on the real axis.

TL;DR: In this paper, an algorithm for the numerical solution of multipoint boundary value problems arising from systems of ordinary differential equations in which jump discontinuities are permitted and for which both the dynamics and boundary conditions may be nonlinear.

TL;DR: In this paper, the reliability, stability and accuracy of determining the polynomials which define the Pade approximation to a given function h(x) by solving a system of linear equations to get the coefficients in the denominator polynomial B n (x) are explored.

TL;DR: In this article, the determinant representations for the two-point Pade approximants are given and the existence of various three-term recursion relations for the numerators and denominators of these approximations is shown.

TL;DR: In this article, the poles of functions represented by continued fractions whose approximants lie on the main diagonal of two-point Pade tables are computed simultaneously, and sufficient conditions are given to ensure that the computations can be carried out and that the resulting approximations converge to the desired poles.

TL;DR: In this paper, a class of end conditions for cubic spline interpolation at unequally spaced knots is derived, which lead to 0 (h 4 ) convergence uniformly on the interval of interpolation.

TL;DR: The (single-point exchange) Remez algorithm is used to obtain the best approximation on a finite set of functions with an alternating characterization of best Chebyshev approximations.

TL;DR: In this article, the usual Sturmanian sequence for finding the eigenvalues of a tridiagonal matrix arising from the radial Schroedinger equation is found to be unstable and a self-stabilising continued fraction approach is suggested.

TL;DR: The purpose of this paper is to address the computational characteristics which would concern a system designer in the consideration of the selection of an effective algorithm to implement a two-point boundary value problem solution.

TL;DR: In this article, the authors give a proof for convergence of the initial value adjusting method, described in detail in part I, based on Kantorovich's theorem, under standard assumptions on the dynamics, boundary conditions, and initial approximations, a quadratic convergence rate is obtained.

TL;DR: In this paper, a collocation method which uses Hermite cubic elements is proposed for the solution of Volterra integrodifferential equations with singular kernels, and the optimum error estimates in the uniform norm are obtained by means of interpolation operators.

TL;DR: In this article, the problem of non-linear convection in a compressible layer with polytropic structure was considered and a single mode expansion was used to obtain a simpler model, within the framework of the anelastic approximation.

TL;DR: An algorithm for rational interpolation that reduces essentially to the Q.D. algorithm for Pade´approximation if the interpolation points are confluent is presented.

TL;DR: In this article, the construction of three-point finite difference approximations for the class of two-point boundary value problems is discussed, and a family of fourth-order discretizations for the differential equations are obtained.

TL;DR: In this article, a Monte Carlo method for solving systems of nonlinear equations is presented and discussed, which does not require the differentiation of left side functions of the system and provides the solution with arbitrary accuracy, although it may be applied only to systems with not too large a number of equations.

TL;DR: In this article, the authors established results of high accuracy for the two-point boundary value problem and derived a derivation of the approximation for large n 3 for the case n is real and positive.

TL;DR: In this paper, a high order perturbation solution of the electrochemical smoothing problem is investigated, which is found to diverge for large time periods unless a reinitialization is attempted.

TL;DR: In this paper, the definition of rational Runge-Kutta methods for systems of equations is given and the equations associated with those methods are solved for the second, third and fourth order.

TL;DR: It is shown how the attainable minimum for the memory requirements of Runge-Kutta methods can be realised for methods of the third order.

TL;DR: In this paper, the Laplace transform is used to eliminate the time-dependency and to produce a subsidiary equation which is then solved in complex arithmetic by finite difference methods, which obviates the need to evaluate the solution at a large number of unwanted intermediate time points.

TL;DR: In this article, an efficient technique for deriving an interpolation polynomial as well as a useful error analysis is presented. But this approach is not suitable for the complex domain.