Fourth-order recursion operators for third-order evolution equations

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Third-order Efficiency Implies Fourth-order Efficiency

Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any rst-order ecient estimators are second-order ecient. Many authors e.g., Ghosh [15], have conjectured that any third-order ecient estimators are fourth-order ecient. Based on concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved expone...

Fourth Order Equations In

Fourth Order Conservative Exponential Methods for Linear Evolution Equations

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order methods allow large step sizes for highly oscillatory equations when the evolution operators vary slowly in time. The methods are also conservative for equations such as the Schrr odinger equation, where the evolution operator is skew-selfadjoint.

Spectral estimates for periodic fourth order operators

We consider the operator H = d 4 dt4 + d dtp d dt + q with 1-periodic coefficients on the real line. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms of the Lyapunov function, which is analytic on a two-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov...