In this paper, two numerical integration methods for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), namely “Third Order One Step Scheme (TOOSS) and Second (SOOSS)” have been considered. The order of convergence, consistency the stability properties schemes investigated. From analyses, it is observed that SOOSS TOOSS second convergence third respecti...

In order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like equations have combined obtain new algorithms. By this combination, powerful hybrid obtained. Necessary conditions for convergence these Furthermore, stability analysis both algorithms is investigated. These applied solving real stiff ordinary...

Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied Physics and Engineering. For example, these equations play a fundamental role in Control Theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-lineari...

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE ...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...