Showing papers in "Journal of Computational and Applied Mathematics in 1992"

TL;DR: In this paper, a method for reconstructing the complex index of refraction of a bounded two-dimensional inhomogeneous object of known geometric configuration from measured scattered field data is presented, which is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive over-relaxation technique.

TL;DR: In this paper, it was shown that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

TL;DR: In this article, the authors consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body and study the full set of Maxwell's equations that govern time-harmonic electric and magnetic fields.

TL;DR: In this article, the Lagrange polynomial interpolation on the nodes of Gauss type quadrature formulas is studied and asymptotic error estimates of the same order as the distance to the best fit are derived.

TL;DR: The sphere packing problem as mentioned in this paper asks whether any packing of spheres of equal radius in three dimensions has density exceeding that of the face-centered-cubic lattice packing (of density φ 18 ).

TL;DR: Two quasi-minimal residual methods for solving non-Hermitian linear systems have been proposed, which — unlike GMRES — are based on short recurrences and hence can be used as true iterative schemes, without restarts.

TL;DR: In this paper, necessary and sufficient conditions for a critical point of certain two-dimensional cubic differential systems to be a centre are presented. But the REDUCE system is not used for the problem of finding the center of such systems.

TL;DR: In this article, the quadrature method for Cauchy-type singular integral equations on [-1, 1] with an additional logarithmic singularity of the kernel is presented.

TL;DR: In this article, formal series solutions are obtained for the difference equation y(n+2)+a(n)y(n+)n+1)+b(n), where a n and b n have asymptotic expansions of the form a n ∼∑ ∞ s = 0 a s n s and b b n √ ∞s = 0 b n n s, for large values of n, and b 0 ≠ 0.

TL;DR: In this article, the authors developed algorithms based on coefficient approximation for the automatic solution of regular and singular Sturm-Liouville problems, and they proved that coefficient approximation can be used to find the solution of the singular singular problem.

TL;DR: In this article, a uniform quartic polynomial spline function is derived via consistency relations connecting the quartic spline values at midknots and the corresponding values of the second and fourth derivatives, respectively.

TL;DR: Two-step sixth-order methods with phase-lag of order eight, ten and twelve were developed for the numerical integration of the special second-order initial-value sproblem.

TL;DR: The average number of nodes in a stratum of random plane-oriented recursive trees is found and it is shown that the limiting distribution of the normalized depth of this node is the standard normal distribution.

TL;DR: Panovsky and Richardson as mentioned in this paper proposed a family of symmetric two-step hybrid methods based on the extrema of the Chebyshev polynomial of degree n. The stability properties of each method are determined by the roots of a quadratic equation λ 2 − 2 α n λ + 1 = 0 where α n ( ν 2 ) is a rational approximation for cos ν.

TL;DR: In this paper, the authors estimate distances between two soft obstacles in terms of corresponding scattering amplitudes using estimates for continuation of solutions of elliptic equations and some methods of potential theory.

TL;DR: In this article, the shape of an impenetrable sound-soft obstacle is determined from the knowledge of a time-harmonic incident plane acoustic wave and far-field or near-field measurements of the scattered wave.

TL;DR: The s-step biorthogonal Lanczos method for finding a few eigenvalues of a large sparse nonsymmetric matrix is introduced, and it is proved that the s- step method generates reduction matrices which are similar to reductionMatrices generated by the standard method.

TL;DR: Murthy et al. as discussed by the authors used the Runge-Kutta-Chebyshev method to solve non-classical parabolic initial-boundary value problems with nonlocal integral terms over the spatial domain.

TL;DR: By expressing the error term in truncation of the asymptotic expansion in terms of a Mellin-Barnes integral, this paper obtained an exponentially improved version of Dingle's result for Γ(z) as ∣z ∣ → ∞ in ∣ arg z ∣ < π.

TL;DR: In this paper, Bender and Richmond's central and local limit theorems are extended to cover a wider class of generating functions, which will cover the above-mentioned combinatorial structures.

TL;DR: In this article, the authors studied orthogonal polynomials (pn) which arise from a given system of orthogonomials by a finite perturbation of the recurrence coefficients.

TL;DR: A simple, efficient and reliable method for computing bases of sets induced by interpolation conditions by so-called transfer matrices is derived.

TL;DR: In this paper, the convergence of derivatives of Lagrange interpolation at the union of zeros of Jacobi polynomials and some additional points is investigated, and it is shown that the convergence is uniform.

TL;DR: In this paper, the nonoscillatory and nonsingular part of the integrand is replaced by a truncated Chebyshev series approximation and the integral is then evaluated using recurrence relations.

TL;DR: A detailed account of what happened in the theory of mean convergence of Lagrange and Hermite-Fejer type interpolation in the last fifty-five years is given in this paper.

TL;DR: In this paper, Erdős and Turan studied the mean convergence of Lagrange interpolation on an extended set of nodes that includes, in addition to the n zeros of the orthagonal (relative to some positive weight function w) polynomial πn of degree n, other n+1 nodes, which in turn are zeros corresponding to the weight functions w n =π 2 n w.

TL;DR: In this article, an alternative theory for functions defined by Mellin-Barnes integrals is presented, which enables uniform exponentially-improved expansions to be established in a direct manner, including estimates for the remainder term in the exponentially small series.

TL;DR: In this article, higher-order, higher-index Hessenberg systems of initial and boundary value differential-algebraic equations (DAEs) are considered and a projected invariant method is proposed.

TL;DR: Sideridis and Simos as mentioned in this paper developed an embedded Runge-Kutta-Fehlberg method for numerical solution of differential equations with periodic solution, using variable stepsize.

TL;DR: In this paper, a collocation method for a first-kind integral equation with a hypersingular kernel on an interval is analyzed, and Sobolev norms are introduced to reflect the singular structure of the exact solution at the endpoints of the interval.