Showing papers in "Journal of Computational and Applied Mathematics in 1986"

TL;DR: In this article, it was shown that if the Noumerov-type methods of [2] are made explicit with the help of the classical second order method, then there exists a selection of the free parameter for which the resulting method has a considerably small frequency distortion of size ( 1 40320 )H 6 and also a (slightly) larger interval of periodicity of size 2.71 for the implicit method.

TL;DR: In this paper, a simple situation of a scalar function where no singular blocks appear in the Pade table is described, and extensions to the matrix case and the multivariable case are discussed in detail.

TL;DR: This work shows how one step of the shifted QR algorithm for H can be carried out in O( n ) arithmetic operations, coupled with the shift strategy of Eberlein and Huang, to permit computation of the spectrum of H, to machine precision, in O 2 operations.

TL;DR: In this article, a new family of two-step fourth-order methods for the test equation is presented, which are P-stable and have a phase-lag of order H6 (H = λh, h is the step size).

TL;DR: There are some values of the (free) parameters available in the methods proposed which can reduce this work of symmetric (hybrid) two-step fourth order P-stable methods to two function evaluations per step.

TL;DR: The RK5(4) and RK6(5) embedded Runge-Kutta formulae are reconsidered with regard to enlarging regions of absolute stability while retaining satisfactory truncation error norms as mentioned in this paper.

TL;DR: A new method to compute the Riemann mapping function is numerically implemented and tested on examples and shows the algorithm to be effective and stable.

TL;DR: In this paper, the exact convergence rate of subdivision algorithms for various settings of polynomial and spline curve or surface representations is investigated. But the convergence rate is not known.

TL;DR: In this paper, a polynomial basis function is used to solve the least square problem, where the unknowns aj(x), the interpolant and the interpolation error are expressed in terms of moving convex combinations of functions corresponding to those of classical interpolation at q + 1 points with respect to these basis functions.

TL;DR: A unified treatment of methods for computing conformal maps from the unit disk onto a Jordan region is presented in this article, where integral and integro-differential equations for the boundary correspondence function are first derived using an arbitrary auxiliary function having certain properties.

TL;DR: In this article, a fast iterative method for solving Fredholm integral equations of the first kind whose kernels have a logarithmic principal part was described. But the method is a Fourier-Galerkin method, and due to the singularity of the kernel, the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative algorithm.

TL;DR: In this paper, the authors consider Laplace's equation in a polygonal domain together with the boundary conditions that along each side, the derivative in the direction at a specified oblique angle from the normal should be zero.

TL;DR: In this article, a class of upper bounds for the positive roots of a polynomial is discussed, and it is shown that the bound (15) is nearly optimal in this class.

TL;DR: In this article, the weight functions and orthogonality relations corresponding to the sequences of polynomials of the second kind associated with the Jacoby and the Gegenbauer poynomials are studied.

TL;DR: In this article, a new class of explicit two-step fourth-order methods for numerical integration of second order initial value problems was introduced, and the authors showed that a method of this family which is based on m + 2 evaluations of f when applied to the test equation possesses an interval of periodicity of length very nearly 2((m + 1)(m + 3)) 1 2 ).

TL;DR: In this article, the authors describe numerical experience on the use of variational inequalities and Pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity, like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle.

TL;DR: For initial value problems in ordinary second-order differential equations of the special form y = f (x, y), explicit, direct Runge-Kutta-Nystrom formula-pairs of order 8(7), 9(8), 10(9) and 11(10) are presented using the mode of Bettis, Dormand and Prince as discussed by the authors.

TL;DR: In this paper, a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon is presented. But this integral does not solve the conformal mapping problem.

TL;DR: In this paper, an iterative method for the calculation of the boundary values of the conformal mapping of a simply connected region G onto a region H with smooth boundary is discussed.

TL;DR: In this paper, the authors derived some inequalities for the cylinder function Cν(x, α) defined by Bessel functions of the first and second kind, respectively, and derived three recurrence relations and an integral formula for the function.

TL;DR: In this paper, an iterative method is described for the determination of the conformal mapping of a circular annulus Rq ≔ {z:q < |z| < 1} onto a doubly connected region G with smooth boundary curves.

TL;DR: In this paper, a report of recent developments concerning the nature and the treatment of singularities that affect certain numerical conformal mapping techniques is given, and some new results on the nature of singularity that the mapping function may have in the complement of the closure of the domain under consideration.

TL;DR: In this article, a multivariate normal integral with tridiagonal covariance matrix can be computed efficiently using iterated integration, where the covariance matrices can be expressed as a linear combination of

TL;DR: In this paper, a simple approximate formula is derived for the boundary map function of a conformal map which provides a remarkably good fit for mappings to regions with highly distorted boundaries, based on the reduction of a nonlocal integral equation for the map function to a local equation.

TL;DR: The convergence order of the proposed methods is five and six respectively as discussed by the authors, and the lower bounds of the R-order of convergence and the convergence conditions for the accelerated (single-step) methods are given.

TL;DR: In this paper, the convergence of the Newton method for the Theodorsen integral equation in conformal mapping is established under certain assumptions on the Riemann-Hilbert problem.

TL;DR: In this article, the convergence of iterative process in R n, of the type x k + 1 = Φ (x k, w k ) was analyzed, and the local convergence of a sequential Kaczmarz type method and a parallel Kachmarz Type method for solving underdetermined systems of nonlinear equations was proved.

TL;DR: In this paper, a Fredholm integral equation of the second kind for the derivative of the boundary correspondence function of the conformal mapping of a Jordan region with piecewise twice differentiable boundary onto the unit disk is presented.

TL;DR: In this article, fast methods for the conformal mapping of simply, doubly and multiply connected regions onto certain canonical regions in the plane are presented, using fast Poisson solvers.

TL;DR: It is shown that for the problems mentioned the convergence factor of the classical Uzawa-algorithm is independent of h, and estimates of the convergence factors which are optimal with respect to the discretization parameter h.