Showing papers in "Journal of Computational and Applied Mathematics in 1998"

TL;DR: In this paper, the American early exercise constraint is used to enforce the penalty source term in the discrete equations of the American chooser option, which can be viewed as transforming the original linear two-dimensional stochastic volatility option pricing PDE into a nonlinear source term.

TL;DR: In this paper, the authors dealt with quasilinear reaction-diffusion equations for which a solution local in time exists and the problem of determining whether the solution ceases to exist for some finite time is studied.

TL;DR: In this paper, a survey of the application of multiple orthogonal polynomials and analytic theory of two model families of general MOPs, referred to as Angelesco and Nikishin systems, is presented.

TL;DR: The FORTRAN program RKC as discussed by the authors is based on a family of Runge-Kutta-Chebyshev formulas with a stability bound that is quadratic in the number of stages.

TL;DR: A new method for numerical integration of C α functions defined on a convex subset C of Rd with respect to a continuous distribution μ, which relies on a space quantization of C by a n-tuplex:=(x1,…,xn) ∈ Cn.

TL;DR: In this article, conditions for matrices A, B, C, D, C so that the series representation of the hypergeometric function be convergent for ¦z¦ = 1 and satisfies a matrix differential equation are given.

TL;DR: In this paper, the Hermite matrix polynomials are used to approximate matrix functions appearing in the solution of differential systems in terms of the three-term recurrence formula.

TL;DR: In this article, a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation is possible is presented.

TL;DR: In this paper, a class of a posteriori error indicators for an electromagnetic scattering problem for Maxwell's equations in the presence of a bounded, inhomogeneous and anisotropic scatterer is analyzed.

TL;DR: Liouville's fractional integration is used to define polygamma functions for negative integer n as mentioned in this paper, which can be represented in a closed form by means of the first derivatives of the Hurwitz Zeta function.

TL;DR: In this article, the stability and instability of a reaction-diffusion equation with nonlocal boundary condition was studied. But the authors focused on the stability of the solution and not on the decay property of the solutions.

TL;DR: In this paper, it was shown that when the space dimension N is equal to three, (S) has radial solutions with finite mass that blow-up in finite time in a self-similar manner.

TL;DR: In this article, a domain decomposition approach for the coupling of Boltzmann and Euler equations is presented, which leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains.

TL;DR: In this article, the possibility of spurious poles is studied from the perspective of these orthogonal relations, and the location and distribution of the spurious poles depend on properties of the orthogonality relations.

TL;DR: The CWI test set for IVP solvers as mentioned in this paper is a collection of initial value problems to test solvers for implicit differential equations, which can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application field and numerical mathematics.

TL;DR: In this paper, an electrostatic interpretation of the zeros of a large class of orthogonal polynomials is presented, based on the ideas of Stieltjes.

TL;DR: A mathematical model based on the theory of stochastic differential equations, along with an implicit two-step method which works directly on the given structure of the equations which makes very efficient implementations possible.

TL;DR: In this article, the authors give an overview of recent work on the distribution of zeros of discrete orthogonal polynomials and give a classification of polynomial zeros.

TL;DR: In this article, a linearized implicit finite difference method for the Korteweg-de Vries equation is proposed and straightforwardly extended to the Kadomtsev-Petviashvili equation.

TL;DR: A new approach of iterative Monte Carlo algorithms for the well-known inverse matrix problem is presented and studied, based on a special techniques of iteration parameter choice, which allows to control the convergence of the algorithm for any column (row) of the matrix using different relaxation parameters.

TL;DR: In this article, the authors considered the discrete focal boundary value problem and proved the existence of three positive solutions under various assumptions on f and the integers a, t2, and b. To prove their results, they used fixed point theorems concerning cones in a Banach space.

TL;DR: A 2-block SOR method and a 3-blockSOR method are proposed to solve the rank-deficient problem and the convergence of the block SOR methods is studied.

TL;DR: In this paper, the authors studied close-to-convexity and univalency of normalized analytic functions in the unit disk and gave conditions on a, b, c and β such that φ satisfies Re e iη ((1 − z ) φ ′( z ) − β ) > 0 for all z ∈ Δ and for some real η ∈ ( −1 2 π, 1 2 ).

TL;DR: A variable step size algorithm for the pathwise numerical approximation of solutions to stochastic ordinary differential equations based on a new pair of embedded explicit Runge-Kutta methods of strong order 1.5(1.0), where the difference between approximations defined by the two methods is used for control of the local error.

TL;DR: An analogue of the Hahn theorem for Laurent biorthogonal polynomials (LBP) Pn(z) is studied in this article, where necessary and sufficient conditions (criterion) for derivatives P n (z) = (n + 1) −1 P′ n+1 (z).

TL;DR: In this paper, a two-stage fourth-order P-stable method for y = f (t, y ) is proposed, based on a pair of discretizations in which the displacement is computed using the trapezoidal rule with end point correction and the velocity is computed by suitably modified Simpson's rule.

TL;DR: In this paper, the authors proved the second-order convergence in L∞ norm of the Tsertsvadze's difference scheme for the Kuramoto-Tsuzuki equation.

TL;DR: In this paper, a shallow membrane cap, with an undeformed shape described in cylindrical coordinates by z = C(1−rγ), is subjected to a uniform vertical pressure P. If the resulting deformed shape is radially symmetric, then under certain assumptions, the radial stress Sr satisfies the ordinary differential equation r 2 S r ″ + 3rS r ′ = λ 2 r 2y−2 2 + βvr 2S r − r 2 8S r 2, for 0 0 (if the boundary stress S is specified) or S

TL;DR: In this paper, the strong asymptotics for the class of Krawtchouk polynomials on the real line were derived and shown to describe the limiting distribution of the zeros of the krawchkouk coefficients.

TL;DR: In this paper, the expansion coefficients of xm and xmqj(x), m∈N0, in series of the set ∗p n (x)∗ are found in terms of the polynomials σ(x) and τ(x).