A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...

I worked with the students in my one-semester graduate course CS615 “Numerical methods for partial differential equations” at Purdue University to write a set of routines to use the finite element method to solve elliptic and parabolic partial differential equations (PDEs). We used hacked versions of gcc-2.95.1, the Gambit-C 3.0 Scheme system by Marc Feeley, and the Meroon object system by Chri...

This paper describes a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution equation for the magnetic field that can be solved using an implicit scheme. This avoids the severe restriction on the stable timestep that would otherwise ar...

We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point is subject to a constraint: it must stay inside a closed set K with boundary of class C. We assume that, at impact, the tangential component of the impulsion is conserved, while its normal coordinate is reflected and multipl...

The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by a uniformly prox-regular set. After obtaining well-posedness results, we propose a numerical scheme based on a predictioncorrection algorithm and we prove its convergence. Finally we apply these results to a problem coming from modelling of crowd ...

Introduction Conclusions References

Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular pe...

An algorithm is presented to numerically treat a free boundary problem arising in the theory of phase transition. The problem is one in which a collection of simple closed curves (particles) evolves in such a way that the enclosed area remains constant while the total arclength decreases. Material is transported between particles and within particles by diiusion, driven by curvature which expre...

We consider numerical approximations to the quantile hedging price of a European claim in nonlinear market with Markovian dynamics. study an equivalent stochastic target problem conditional probability success as new state variable, addition asset value process. propose based on piecewise constant policy time stepping coupled novel finite difference schemes. prove convergence monotone case comb...

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...