Showing papers in "Journal of Computational and Applied Mathematics in 2002"

TL;DR: In this article, the authors give an introduction to the time scales calculus, and present various properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equations of first order.

TL;DR: In this article, a form of self-adjoint differential equations on time scales so that the associated Green's function is found symmetric in the usual sense is presented. And the concepts of Lebesgue delta and nabla integrals are introduced.

TL;DR: In this article, the authors presented new symmetric fourth and sixth-order symplectic partitioned Runge-Kutta and Runge Kutta-Nystrom methods.

TL;DR: In this paper, an efficient method for the multivariate interpolation of very large scattered data sets is presented based on the local use of radial basis functions and represents a further improvement of the well known Shepard's method.

TL;DR: In this paper, the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional equations each of order at most unity.

TL;DR: In this paper, a review of buoyancy-driven flows arising from the sudden release of a fixed volume of heavy fluid into a larger body of less dense ambient fluid is presented.

TL;DR: In this article, necessary and sufficient conditions are given for two sequences λn and ρn to be the eigenvalues and norming constants of a Sturm-Liouville boundary value problem, where f is a rational function of Herglotz-Nevanlinna type.

TL;DR: It is shown that the total ordinal rank of objects may produce a different result according to the difference of the weights between ranks, and a new ordering to solve the weights of ranks is proposed by considering feasible solutions' region of the constraint set in LP.

TL;DR: In this paper, it was shown that in the evolution of the random d-uniform hypergraph Gd(n,M) the phase transition occurs when M = n/d(d - 1) + O(n2/3).

TL;DR: In this paper, the authors consider the linear multistep algorithms for first order ODEs and examine the problem of how the λ-frequencies should be tuned in order to obtain the maximal benefit from the exponential fitting versions of such algorithms.

TL;DR: In this article, the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency is considered.

TL;DR: In this paper, an efficient numerical method for sensitivity computation of large-scale differential algebraic systems is developed based on the adjoint method, which is applicable to applications with a large number of sensitivity parameters and few objective functions.

TL;DR: In this paper, the discretization error of semilinear stochastic evolution equations in Lp-spaces is investigated, and the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme are considered.

TL;DR: In this article, a Dirichlet problem for a system of two coupled singularly perturbed reaction-diffusion ordinary differential equations is examined and a numerical method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameters is constructed and analyzed.

TL;DR: In this paper, the stationary and non-stationary flow of viscous incompressible fluid under boundary conditions of friction type, which are certain nonlinear boundary conditions similar to the so-called Signorini boundary condition in elasticity, are analyzed.

TL;DR: In this paper, three types of methods for integrating periodic initial value problems are presented: phase-fitted, zero dissipation, zero dissipative, and phase fitted with phase-fitting.

TL;DR: The way to obtain deterministic Runge-Kutta methods from Taylor approximations is generalized for stochastic differential equations, now by means of stochastically truncated expansions about a point for sufficiently smooth functions of an Ito process.

TL;DR: In this paper, a personal bird's eye view of some aspects of multivariate numerical integration is given, sketching what happened during the past 50 years and pointing the reader's attention to what did not happen.

TL;DR: In this article, the authors used Lyapunov-like functions to obtain sufficient conditions for the practical stability of hybrid dynamic systems on time scales, and showed that these conditions can be obtained for any dynamic system.

TL;DR: In this article, the authors describe the use of cubic splines for interpolating monotonic data sets and present an energy minimization framework to yield linear and nonlinear optimization-based methods.

TL;DR: Some key technologies employed in the ADVENTURE system are described, and some latest results including elastic stress analysis of a precise three-dimensional model of a nuclear reactor vessel with a 60 million DOF mesh on Hitachi SR2201 (1024 PEs) are shown.

TL;DR: In this article, the second order Sturm-Liouville dynamic equation was investigated on a time scale (r(t)xΔ)Δ + c( t)xσ = 0.

TL;DR: In this article, the authors obtain oscillation criteria for a second-order self-adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function.

TL;DR: In this article, a difference scheme based on cubic spline in compression for second-order singularly perturbed boundary value problem was proposed, which has second and fourth-order convergence depending on the choice of parameters.

TL;DR: Global convergence results are established for unconstrained optimization algorithms that utilize a nonmonotone line search procedure that allows the user to specify a flexible forcing function and includes the non monotone Armijo rule, the nonMonotone Goldstein rule, and the non Monotone Wolfe rule as special cases.

TL;DR: In this paper, the authors derived an asymptotic error expansion of the iterated discrete Galerkin solution, which covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth.

TL;DR: In this article, the existence of maximal and minimal solutions of the periodic boundary value problem for first-order impulsive functional differential equations is considered by means of upper and lower solutions and the monotone iterative technique.

TL;DR: In this article, an ad hoc preconditioning technique was devised to handle the differential equations of the reaction-diffusion (R-D) system associated with myocardial excitation process modeling.

TL;DR: In this article, the impact of delay on the existence of traveling wave fronts in reaction-diffusion equations of KPP-Fisher type was explored and it was shown that delay can induce slow traveling wave front.

TL;DR: In this paper, the authors consider slip with friction and penetration with resistance boundary conditions in the steady state Navier-Stokes equations and describe some aspects of the implementation of these boundary conditions for finite element discretizations.