In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization--based integration (QBI), i.e., replacing the time discretization by state quantization, ...

In the present paper we give some necessary conditions that satisfy the solutions of an infinite system of ordinary differential equations. We investigate the behavior of the solutions of a general system of equations, ...

A linear ODE system with bounded continuous coefficients is studied. Provided that the diagonal terms are ‘‘separated’’ and the off-diagonal terms satisfy a smallness threshold, we present some sufficient conditions for ...

This work presents a brief history about the differential equations, followed by definitions, classifications and methods of solutions involving ordinary differential equations. At first, will be presented a brief historical ...

In this work, we will present the coincident degree theory for Fredholm operators of index zero - denoted by L and defined on Banach spaces -, which is an important tool to obtain the existence of solutions for equations ...

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the ...

A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, ...