We present several algorithms to compute invariant tori in a family of dynamical systems using a continuation strategy. The algorithms are based on the discretization of the graph transform. To circumvent two problems of the standard approach (which requires solving ordinary BVPs) we modify the discretized graph transform. This results in faster and more robust methods.

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

For solving nonlinear boundary value problems (BVPs), a main difficulty of using Adomian’s method is to find a canonical form which takes into account all the boundary conditions of the problem. This difficulty is overcome by using a modification for Lesnic’s approach developed in this paper. The effectiveness of the proposed procedure is verified by two nonlinear problems: the nonlinear oscill...

In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODEIVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution ...

In engineering disciplines, many important problems are to be formed as boundary value (BVPs) that have conditions specified at the extremes. To handle such problems, conventional shooting method transforms BVPs into initial has been extensively used, but it does not always guarantee solving problem due possible failure of finding a proper guess. This paper proposes universal guess finder is co...

This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order dynamic equations on time scales subject to two-point boundary conditions. The methods involve novel dynamic inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. AMS subject classification: 39A12, 34B15.

3 Simulation Phase: Three Models for Simulation 9 3.1 3D ChainMail . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Mass Spring Models . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.1 Classical Mass Spring Model . . . . . . . . . . . . . . . 13 3.2.2 Fast Tetrahedral Mass Spring Model . . . . . . . . . . 15 3.3 Finite Element Models . . . . . . . . . . . . . . . . . . . . . . 1...

This article investigates the existence of solutions to first-order, nonlinear boundary value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods. AMS 2000 Classification: 34B15, 34B99

This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order ordinary differential equations and two-point, periodic boundary conditions. The methods involve novel differential inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. AMS 2000 Classification: 34B15