15 research outputs found
Methods in Mathematica for Solving Ordinary Differential Equations
An overview of the solution methods for ordinary differential equations in
the Mathematica function DSolve is presented.Comment: 13 page
Computation of conservation laws for nonlinear lattices
An algorithm to compute polynomial conserved densities of polynomial
nonlinear lattices is presented. The algorithm is implemented in Mathematica
and can be used as an automated integrability test. With the code diffdens.m,
conserved densities are obtained for several well-known lattice equations. For
systems with parameters, the code allows one to determine the conditions on
these parameters so that a sequence of conservation laws exist.Comment: To appear in Physica D, 17 pages, Latex, uses the style files
elsart.sty and elsart12.st
Computation of conserved densities for systems of nonlinear differential-difference equations
A new method for the computation of conserved densities of nonlinear
differential-difference equations is applied to Toda lattices and
discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations.
The algorithm, which can be implemented in computer algebra languages such as
Mathematica, can be used as an indicator of integrability.Comment: submitted to Phys. Lett A, 10 pages, late
Algorithmic Integrability Tests for Nonlinear Differential and Lattice Equations
Three symbolic algorithms for testing the integrability of polynomial systems
of partial differential and differential-difference equations are presented.
The first algorithm is the well-known Painlev\'e test, which is applicable to
polynomial systems of ordinary and partial differential equations. The second
and third algorithms allow one to explicitly compute polynomial conserved
densities and higher-order symmetries of nonlinear evolution and lattice
equations.
The first algorithm is implemented in the symbolic syntax of both Macsyma and
Mathematica. The second and third algorithms are available in Mathematica. The
codes can be used for computer-aided integrability testing of nonlinear
differential and lattice equations as they occur in various branches of the
sciences and engineering. Applied to systems with parameters, the codes can
determine the conditions on the parameters so that the systems pass the
Painlev\'e test, or admit a sequence of conserved densities or higher-order
symmetries.Comment: Submitted to: Computer Physics Communications, Latex, uses the style
files elsart.sty and elsart12.st
Application of perturbation–iteration method to Lotka–Volterra equations
Perturbation–iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka–Volterra systems are obtained using the method. Comparisons of our results with each other and with numerical solutions are given. The method is implemented in Mathematica, a major computer algebra system. The package PerturbationIteration.m automatically carries out the tedious calculations of the method
Application of pert
Perturbation–iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka–Volterra systems are obtained using the method. Comparisons of our results with each other and with numerical solutions are given. The method is implemented in Mathematica, a major computer algebra system. The package PerturbationIteration.m automatically carries out the tedious calculations of the method