this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modi ed Korteweg de Vries CMKdV equation are reported The rst is an integrable scheme derived by methods related to the Inverse Scattering Transform IST The second is derived from the rst and is called the local IST scheme The third is a standard nite di erence scheme for the CMKdV equation Trav...

We consider the parabolic approximation to the three{dimensional Helmholtz equation for the acoustic pressure. The parabolic equation is semi{discretized in the range variable using an implicit scheme (e.g., Crank{Nicolson). This leads to a complex elliptic partial di erential equation that must be solved at each range step. We use a multigrid method to solve this partial di erential equation, ...

We propose a new method for evaluating the security of block ciphers against di erential cryptanalysis and propose new structures for block ciphers. To this end, we de ne the word-wise Markov (Feistel) cipher and random output-di erential (Feistel) cipher and clarify the relations among the di erential, the truncated di erential and the impossible di erential cryptanalyses of the random output-...

It is proven that an initial value problem of an autonomous system verifying some conditions has exactly one open continuously di€erentiable trajectory on R, whose limit set is not one point. The proof of the result is based upon continuation methods. 1. Preliminaries Di€erential equations play a key role in nature and technology because they control their processes. In time-dependent processes...

Multigrid methods are studied for the solution of linear systems resulting from the 9-point discretization of a general linear second-order elliptic partial di erential equation in two dimensions. The rate of convergence of standard multigrid methods often deteriorates when the coe cients in the di erential equation are discontinuous, or when dominating rst-order terms are present. These di cul...

This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the Mc Kean Vlasov equation introduce d by Bossy and Talay. More speci cally, we consider approximations of the distribution and of the density of the solution of the stochastic di erential equation associated to the Mc Kean Vlasov equation. The scheme adopted here is a mixed one: Euler/weakly ...

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

. We consider a multivariate continuous time process, generated by a system of linear stochastic di¤erential equations, driven by white noise and involving coe¢ cients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing signi…cantly simpli…es matters). Such settings represent partial extensions of ones s...

Observers are usually formulated as explicit systems of di erential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Di erential-Algebraic Equation). We review the general idea of DAE observer design of [10]. We give two special normal forms for which DAE observer design yields an observer with linear...