Solving Initial Value Problems for Ordinary Differential Equations by two approaches: BDF and piecewise-linearized methods

Solving Initial Value Problems for Ordinary Differential Equations by two approaches: BDF and piecewise-linearized methods

Piecewise-linearized methods for initial-value problems with oscillating solutions

Two piecewise-linearized methods for the numerical solution of nonlinear second-order differential equations which contain the first-order derivative are presented. These methods provide piecewise analytical solutions in open intervals, result in explicit finite difference equations for both the displacement and the velocity or only the displacement, at nodal points, and continuous solutions ev...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

Solving Differential Riccati Equations Using BDF Methods

This technical report describes three approaches for solving the Differential Riccati Equation (DRE), by means of the Backward Differentiation Formula (BDF) and resolution of the corresponding implicit equation, using Newton's method. These approaches are based on: GMRES method, resolution of Sylvester equation and fixed point method. The role and use of DRE is especially important in optimal c...

Validated solutions of initial value problems for ordinary differential equations

Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated so...