Showing papers in "Journal of Computational and Applied Mathematics in 1984"

TL;DR: A numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented in this article, where the disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the Discretization error, a method for accelerating the convergence of the Fourier Series and a procedure that computes approximately the "best" choice of the free parameter.

TL;DR: The author's decomposition method as mentioned in this paper provides a new, efficient computational procedure for solving large classes of nonlinear (and/or stochastic) equations, including differential equations containing polynomial, exponential, and trigonometric terms, negative or irrational powers, and product nonlinearities.

TL;DR: In this paper, the authors considered a fourth order nonlinear ordinary differential equation with two-point boundary conditions and provided apriori error estimates on the length of the interval (b−a) so that the Picard's iterative method, the approximate Picard's method and the quasilinear method converged to the solution of the problem.

TL;DR: In this paper, the stability properties of numerical methods for delay differential equations are considered and suitable definitions for the stability of the numerical methods are included and Runge-Kutta type methods satisfying these properties are tested on a numerical example.

TL;DR: In this article, the authors adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in Euclidean spaces, which is made simple and efficient for numerical computation.

TL;DR: In this paper, the construction and convergence of high-order product integration methods for the second-kind Abel equation are discussed and the results of De Hoog and Weiss are generalised.

TL;DR: This work describes a branch and bound algorithm based on embedding Glover and Klingman's method for the associated linear program within a depth-first search procedure for the multiple-choice knapsack problem.

TL;DR: In this article, the authors considered the construction of methods based on trigonometric polynomials for the initial value problems whose solutions are known to be periodic, assuming that the frequency w can be estimated in advance.

TL;DR: In this article, the stability regions of linear multistep methods for pure delay equations are compared with the stability region of the delay equation itself, and a criterion is derived stating when the numerical stability region contains the analytical stability region.

TL;DR: In this article, the author's decomposition method using A n polynomials for the nonlinearities has been shown to apply to wide classes of nonlinear (or nonlinear stochastic) operator equations providing a computable, accurate solution which converges rapidly.

TL;DR: In this article, the Clausen integral Cl2(Θ) is expressed in terms of known constants and special functions when Θ is equal to a rational multiple of π belonging to [0, 2π] and the sine function is deduced from an appropriate Fourier series expansion.

TL;DR: For a given summability method, the Okada theorem describes a domain into which an arbitrary power series can be analytically continued, if such a domain is known for the geometric series.

TL;DR: In this article, a new class of outer approximation methods for solving general convex programs is presented, which solve at each iteration a subproblem whose constraints contain the feasible set of the original problem.

TL;DR: In this paper, the quality of error estimators is studied in this situatuion, and it is shown how to modify unsatisfactory estimators so as to improve them greatly, using several formulas from the literature.

TL;DR: In this paper, the Clausen integral Cl 2 (Θ) = −∫ Θ 0 ln(2 sin t 2 ) d t whereby Θ is equal to a rational multiple of π belonging to ] 0,2π[, is developed into a finite series of derivatives of the di-gamma function ψ.

TL;DR: In this paper, an error bound for product quadrature rules based on cubic B-splines is provided, and examples that test the performance of these rules for different choices of the function are given.

TL;DR: In this paper, the critical lengths of the domain at which bifurcation occurs in the cases b = 0, a and 1 were estimated and the non constant steady state solutions which appear beyond the points of instability were characterised.

TL;DR: In this paper, the exact evaluation of three single integrals relating to the dielectric behavior of two-dimensional electron plasmas was presented, and a procedure for reducing 3D-dimensional integrals of the form: ∫∫ ∫ d q d p d k D(q)α( p + k + q + q )ƒ( p )[1− ǫ( p+ǫ + q )]

TL;DR: In this paper, four general principles are proposed for use in constructing convergence speeding methods and five old methods and about 15 more recent non-linear methods are discussed with reference to their range of applicability and rate of convergence speeding when applied to alternating, monotonic, slightly erratic, Fourier and alternating divergent series.

TL;DR: In this paper, the authors consider the problem of determining the main singularities of the function H in compl( Ω∪∂Ω ) and provide information regarding the location and nature of such singularities, which can be used to improve the efficiency of certain expansion methods for numerical conformal mapping.

TL;DR: In this paper, it was shown that the approximation properties of l k, h μ are completely governed by those of the space spanned by the translates of all so-called box splines contained in L k,h μ.

TL;DR: It is shown that rational RK-methods are not very appropriate to solve stiff differential equations and the stepsizes which can be expected when solving a stiff differential system with a rational or with an explicit linear Rk-method are of the same order of magnitude.

TL;DR: Boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations as mentioned in this paper, for which complete families of particular solutions are explicitly known, and the method contains various decisions which are important for its performance, such as choice of solution subspace, choice of basis for the subspace.

TL;DR: The algorithms of Levinson-Schur and Nevanlinna-Pick are briefly reviewed in this article, where they produce least squares predictive filters by minimizing the least square error with respect to the interpolation points of the NevANP algorithm.

TL;DR: Since the MIN-MAX Algorithm attains the optimal minimized delay assignment by minimization of the Min-Max assignment, the aspects of its relation to the MAX-MIN Algorithms, theMin-Max inequality and the of both algorithms offers an option for considering all possible, allowed link assignment combinations of the n capacities available to further minimize delay.

TL;DR: This is a review paper which describes recent advances in numerical methods and computer codes for solving initial value problems of ordinary differential equations, with particular emphasis on stiff systems.

TL;DR: The Fast Approximate Inversion Algorithm of Frederickson is applied to solve a large scale sparse linear system arising from the triangular finite element solution to the second order elliptic problems.

TL;DR: In this article, it was shown that the known infinite continued fraction development of the ratio of Bessel functions Jv−1(z)/Jv(z) gives rise to an orthogonality property of the Lommel polynomials when v is real and positive.

TL;DR: The recursive relations given in Part I of this report can be interpreted as recursions for the denominators of matrix Pade approximants as discussed by the authors, and dual relations for the corresponding numerators and residuals.