Draft version of May 13, 2009 FUNDAMENTAL MATRIX SOLUTIONS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS

Fundamental matrix solutions of piecewise smooth differential systems

We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more su...

Self-similar solutions‎ ‎of the Riemann problem for two-dimensional systems of conservation‎ ‎laws

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

A Piecewise Approximate Method for Solving Second Order Fuzzy Differential Equations Under Generalized ‎Differentiability‎

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...