A Maple package for verifying ultradiscrete soliton solutions

We present a Computer algebra program for verifying soliton solutions of ultradiscrete equations in which both dependent and independent variables take discrete values. The package is applicable to equations and solutions that include the max function. The program is implemented using Maple software. Program summary Program title: Ultde Catalogue identifier: AEDB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3171 No. of bytes in distributed program, including test data, etc.: 13633 Distribution format: tar.gz Programming language: Maple 10 Computer: PC/AT compatible machine Operating system: Windows 2000, Windows XP RAM: Depends on the problem: minimum about 1 GB Wordsize: 32 bits Classification: 5 Nature of problem: The existence of multi-soliton solutions strongly suggest the integrability of nonlinear evolution equations. However enormous calculation is required to verify multi-soliton solutions of ultradiscrete equations. The use of computer algebra can be helpful in such calculations. Solution method: Simplification by using the properties of max-plus algebra. Restrictions: The program can only handle single ultradiscrete equations. Running time: Depends on the complexity of the equation and solution. For the examples included in the distribution the run times are as follows. (Core 2 Duo 3 GHz, Windows XP) Example 1: 2725 sec. Example 2: 33 sec. Example 3: 1 se

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described