We design here a primary platform for computing the basic homological information of Commutative Di erential Graded Algebras (brie y, CDGAs), endowed with linear di erential. All the algorithms have been implemented in the framework settled by Mathematica, so that we can take advantage of the use of symbolic computation and many other powerful tools this system provides. Working in the context ...

The intention of this special session on ”Advances in the numerical solution of nonlinear evolution equations” is to gather mathematicians and theoretical physicists, interconnected through their field of application, the analytical tools, or the numerical methods used. The scope of topics includes but is not limited to Schrödinger type equations, highly oscillatory equations, parabolic problem...

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...

In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...

We consider the solution of singular perturbation delay di erential equations (SPDDEs) by using boundary value methods (BVMs). These methods require the solution of some nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We prove that if an Ak1 ; k2 -stable BVM is used for solving a sy...

We present a method to solve initial and boundary value problems using arti ial neural networks. A trial solution of the di erential equation is written as a sum of two parts. The rst part satis es the initial/boundary onditions and ontains no adjustable parameters. The se ond part is onstru ted so as not to a e t the initial/boundary onditions. This part involves a feedforward neural network, ...

This paper concerns a new type of approximant for series analysis. By incorporating linear recurrence techniques, such as are involved with second order di erential approximants, algebraic approximants can be extended to nonlinear di erential approximants. The discussion of nonlinearities is constrained by discussing approximants just one step removed from second order algebraic approximants. T...

Bulk synchronous parallel architectures o er the prospect of achieving both scalable parallel performance and architecture independent parallel software. They provide a robust model on which to base the future development of general purpose parallel computing systems. In this paper we theoretically and experimentally analyse the e ciency with which a wide range of important scienti c computatio...

Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...