Showing papers in "Mathematics and Computers in Simulation in 1994"

TL;DR: In this paper, various symplectic discretizations of the nonlinear Schrodinger equation are compared, including one for the integrable discretization due to Ablowitz and Ladik.

TL;DR: In this paper, an effective iterative procedure for estimating the subject parameter is introduced, which always converges and does not depend on the initial point of the iteration, and it is shown by numerical examples that their method converges faster than the popular Newton-Raphson method.

TL;DR: A new technique, genetic search, is compared to two old techniques the pattern search and the response surface method search, using the Hooke–Jeeves algorithm and the Dennis Smith algorithm for accuracy and stability.

TL;DR: SCARP is a shell that allows to develop problem solving environments providing the necessary cooperation facilities for interactive problem solving, and SLOT, a problem solving environment in exploratory data analysis, developed using SCARP is discussed.

TL;DR: In this paper, three numerical schemes for the numerical simulation of the complex modified Korteweg-de Vries (CMKdV) equation are reported, one is an integrable scheme derived by methods related to the Inverse Scattering Transform (IST).

TL;DR: In this article, simulation methods for the numerical approximation of some linear boundary value problems involving Laplace's operator are presented, which are based on Feyman-Kac representations of the solutions.

TL;DR: The renormalization techniques for determining the long-time asymptotics of nonlinear parabolic equations pioneered by Bricmont, Kupiainen and Lin are shown to be effective in analyzing nonlinear wave equations featuring both dissipation and dispersion as mentioned in this paper.

TL;DR: The SoftLab project attempts to link physical laboratory experimentation with computer control and simulation to provide a virtual laboratory for computational science.

TL;DR: In this paper, the properties of delay functions are studied theoretically and two different methods for the simulation of the delay are derived.

TL;DR: In this paper, the authors extend the well-known split-step Fourier method for solving the nonlinear Schrodinger equation to the Davey-Stewartson system, and discuss both the elliptic-hyperbolic and hyperbolic-elliptic cases, as well as the implementation of boundary conditions.

TL;DR: In this article, the inverse scattering transform (IST) for the periodic Kortweg-de Vries (KdV) equation in the μ-function representation is considered and numerical formulations are given (1) for determining the direct scattering transform spectrum of an input discrete wave train and (2) for reconstructing the wave train from the spectrum via inverse scattering problem.

TL;DR: The author will illustrate the use of GAMS, describe its implementation, and outline plans for the incorporation of expert advisory capabilities.

TL;DR: An AI architecture is proposed which facilitates the expression of knowledge at the level of the SP specialist, and how a given SP problem is solved by the KBS.

TL;DR: In this article, the authors present an analysis of various integration schemes which are applied to the numerical integration of a one-dimensional Hamiltonian system and, second, Painleve equations I and II.

TL;DR: The expert assistant acts as a consultant during the simulations, advising the user in the mesh analysis, the prescription of boundary conditions, the assessment of numerical results, and the choice of the various numerical parameters involved in the simulation.

TL;DR: SHASTRA is a highly extensible, distributed and collaborative design and scientific manipulation environment which is a powerful collaboration substrate to support synchronous multi-user applications and a distribution substrate which emphasizes distributed problem solving.

TL;DR: A comparative study of four optimisation algorithms based on simulated annealing: the Gibbs Sampler, the Metropolis algorithm, the Iterated Conditional Modes, and an original method of random descent proposed by the authors.

TL;DR: Work to develop a robust knowledge-base for the automated construction of numerical algorithms is described, with a target domain for the system is Finite Element Analysis of incompressible fluid dynamics and heat transfer.

TL;DR: Based on singular perturbation analysis of nonlinear PDEs, an approximate solution of the equation is obtained, constructed from a solution ofThe reduced equation associated with the given non linear PDE, and correction terms corresponding to boundary layers and interior layers.

TL;DR: Computational mechanisms for intelligently simulating nonlinear control systems are developed that enhance numerical simulations with deep domain knowledge of dynamical systems theory and control theory, a qualitative phase-space representation of dynamicals systems, symbolic and geometric manipulation capabilities, and a high-level interface.

TL;DR: In this paper, the brachistochrone problem is formulated as a nonlinear optimal control problem and solved using the Legendre-Gauss-Lobatto (GLG) nodes.

TL;DR: To conclude in the possible validity of the simulation, the results provided by the computer must previously be validated.

TL;DR: In this article, eight different approximations to a one-dimensional steady-state boundary-value problem for a general symmetric second-order ordinary differential equation with discontinuous leading coefficient are studied.

TL;DR: In this paper, the Korteweg-de Vries equation is numerically solved by using a new algorithm based on the quintic spline approximation, and an iterative scheme having O(k 2 + kh 2 ) accuracy and five-band constant coefficients system of equations is devised.

TL;DR: It is argued that CBR can provide greater flexibility than the traditional rule-based approach, permitting solutions of problems to be proposed even when domain knowledge is lacking, and coupling this approach with a rule-base can provide a problem solving environment for tackling complex real-world problems.

TL;DR: In this article, the authors proposed numerical schemes for approximating periodic solutions of the generalized Korteweg-de Vries-Burgers equation using a Galerkin-finite element formulation for the spatial discretization and use implicit Runge-Kutta (IRK) methods for time stepping.

TL;DR: An explicit finite difference scheme for the numerical solution of the diffusion equation on a rectangular region, subject to a non-local boundary condition in the form of a double integral which simulates the specificaion of mass in a curved region is developed in this article.

TL;DR: This paper provides two simple results by which complex systems can be identified as sets of interconnected subsystems and their respective interconnections.

TL;DR: A knowledge-based system coupled with a finite element library that guides the user in the specification of the physical problem, finds a correct solution path, and activates numerical modules.