Numerical treatment of a Volterra integral equation with space maps

Mario Annunziato, Eleonora Messina
2010 Applied Numerical Mathematics  
We present numerical schemes for the Liouville Master Equation (LME) associated to a stochastic process that results from the action of a semi-Markov process on first order differential equations. The LME is a system of hyperbolic PDE with both local and non-local boundary conditions. We show that equation in differential and integral form and give a proof for the existence and uniqueness of the solution for the integral form. We use numerical schemes for solving the differential [1; 2] and
more » ... gral form [3]. We study stability by Fourier analysis, and show some numerical experiments on cases of practical application that confirms the theoretical findings. The talk deals with the smoothing -interpolating (smoothing for a part of data and interpolating for the rest) problems in the abstract setting of a Hilbert space. Let X, Y be Hilbert spaces and assume that linear operators T : X → Y , A 1 : X → IR n and A 2 : X → IR m are continuous. We consider the conditional minimization problem ||T x|| −→ min x∈H Abstracts of MMA2010,
doi:10.1016/j.apnum.2010.04.007 fatcat:ufj2wop7l5eqbc5zridfuigtyu