The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by di erential equations with discontinuous right{hand sides. In this paper we analyze the behavior of three di erent Lotka{Volterra predator{prey systems with opt...

in this paper, we consider first-order fuzzy differential equations with initial value conditions. the convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized h-differentiability, are studied. then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

The intention of this special session on ”Advances in the numerical solution of nonlinear evolution equations” is to gather mathematicians and theoretical physicists, interconnected through their field of application, the analytical tools, or the numerical methods used. The scope of topics includes but is not limited to Schrödinger type equations, highly oscillatory equations, parabolic problem...

Numerical solution for ordinary di erential equations (ODEs) is an established research area. There are many well established methods, such as Runge-Kutta methods and multi-step methods, for such purposes. There are also many excellent books on this subject, for example [1], [13] and [17]. Special purpose ODE solvers, such as those for sti ODEs, are also well studied. See, e.g., [6]. However, t...

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

Time dependent partial di erential equations are often solved using algorithms which parallelize the solution process in the spatial domain. However, as the number of processors increases, the parallel e ciency is limited by the increasing communication/computation ratio. Recently, several researchers have proposed algorithms incorporating temporal domain parallelism in order to increase e cien...

Time dependent partial di erential equations are often solved using algorithmswhich parallelize the solution process in the spatial domain. However, as the number of processors increases, the parallel e ciency is limited by the increasing communication/computation ratio. Recently, several researchers have proposed algorithms incorporating time domain parallelism in order to increase e ciency. I...

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...

We consider a ...nancial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for a number of cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of ...rst order parti...