on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

diffusive energy growth in classical and quantum driven oscillators we study the long time stability of oscillators driven by time dependent forces originating from dynamical systems with varying degrees of randomness the asymptotic energy growth is related to ergodic properties of the dynamical system when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy for a system with good mixing properties we obtain a stronger result in the form of a central limit theorem if the autocorrelation decays slowly or does not decay the behavior can depend on subtle properties of the particular model we study this dependence in detail for a family of quasiperiodic forces the solution involves the analysis of a small denominator problem that can be treated by fairly elementary methods in the special case of a periodic force the quantum stability problem can be expressed in terms of spectral properties of the floquet operator in the presence of resonances the spectrum is absolutely continuous we find explicitly the eigenvalues and eigenfunctions for the nonresonant case

convergence analysis of the secant type methods in this paper under the hypothesis that derivative satisfies some kinds of weak lipschitz condition the radius estimates of the convergence balls of secant type methods for operator equations are established in banach space some applications and numerical experiments are also given

a convergence theorem for newton like methods under generalized chen yamamoto type assumptions in this study we provide sufficient conditions for the convergence of a newton like method to a locally unique solution of a nonlinear equation with a nondifferentiable term in a banach space setting we introduce new conditions by assuming the existence of real functions of two variables that serve as upper bounds on the operators involved special choices of the real functions mentioned above lead to chen yamamoto type assumptions or the usual lipschitz conditions associated with the frechet derivatives of the nonlinear operators involved using the majorant method we show that if a certain scalar inequality has a minimum positive solution then the abstract equation has a locally unique solution also we also show that our upper bounds on the distances x n 1 x n and x n x improve on earlier ones found by chen yamamoto dennis rheinboldt and potra et al finally our results can apply to solve nonlinear integral equations of uryson type

improving the applicability of the secant method to solve nonlinear systems of equations a modification of the secant method for the approximation of nonlinear system of equations is considered to improve the applicability of the secant method this modification changes the resolution of a linear system in each step necessary to apply the secant method for several matrix multiplications in this way the numerical stability of the secant method can be improved in addition in this paper we prove that the modification considered keeps two important properties of the secant method such as does not use derivatives in its algorithm and has r order of convergence at least 1 5 2

local convergence of efficient secant type methods for solving nonlinear equations abstract a local convergence analysis for an efficient secant type method stm for solving nonlinear equations is given using both the lipschitz continuous and center lipshchitz continuous divided differences of order one an estimate of the radius of the convergence ball of stm is provided the error estimate matching its convergence order is established numerical examples validating the theoretical results are also provided in the concluding section of this study

ostrowski type methods for solving systems of nonlinear equations abstract four generalized algorithms builded up from ostrowski s method for solving systems of nonlinear equations are written and analyzed a development of an inverse first order divided difference operator for functions of several variables is presented as well as a direct computation of the local order of convergence for these variants of ostrowski s method furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

on the determination of the steady film profile for a non newtonian thin droplet abstract a shooting method is used to determine a solution to a third order ode modeling the steady profile of a non newtonian thin droplet we compare a direct approach to an iterative approach using a secant method we obtain a nonlinear relationship between the contact angle and the position of the contact line r from this nonlinear relationship we use curve fitting to obtain an empirical law of the form tan r f k where k is the power law coefficient and f is a nonlinear function of k

some remarks concerning stability for nonstationary quantum systems the problem of characterizing stability and instability for general nonstationary quantum systems is investigated some characterizations are reported and some elementary properties of a topological characterization are established then it is proven by considering a simple example that there are nonperiodic driven systems whose orbits are neither precompact nor leave on average any compact set autocorrelation measures are computed and the possible roles of the generalizes quasienergy operator and energy growth are briefly discussed

a kantorovich type analysis for a fast iterative method for solving nonlinear equations abstract we revisit a fast iterative method studied by us in i k argyros on a two point newton like method of convergent order two int j comput math 88 2 2005 219 234 to approximate solutions of nonlinear operator equations the method uses only divided differences of order one and two function evaluations per step this time we use a simpler kantorovich type analysis to establish the quadratic convergence of the method in the local as well as the semilocal case moreover we show that in some cases our method compares favorably and can be used in cases where other methods using similar information cannot s amat s busquier v f candela a class of quasi newton generalized steffensen s methods on banach spaces j comput appl math 149 2 2002 397 406 d chen on the convergence of a class of generalized steffensen s iterative procedures and error analysis int j comput math 31 1989 195 203 numerical examples are provided to justify the theoretical results

triangular and rectangular elements in the spectral domain analysis of arbitrarily shaped planar circuits an existing approach for the spectral domain analysis of planar circuits in layered media based on piecewise sinusoidal current expansion functions over rectangular elements which are located parallel or perpendicular to each other is expanded to a wider class of geometric shapes in a first step the rectangular cells are allowed to be arbitrarily directed in the plane of the circuit in a second step triangular elements are used to combine arbitrary rectangular cells two kinds of current expansion functions with different computational effort are applied to the triangular and its two adjacent rectangular elements numerical results are presented

a class of steffensen type methods with optimal order of convergence abstract in this paper a family of steffensen type methods of fourth order convergence for solving nonlinear smooth equations is suggested in the proposed methods a linear combination of divided differences is used to get a better approximation to the derivative of the given function each derivative free member of the family requires only three evaluations of the given function per iteration therefore this class of methods has efficiency index equal to 1 587 kung and traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2 d 1 where d is the number of functional evaluations per step the new class of methods agrees with this conjecture for the case d 3 numerical examples are made to show the performance of the presented methods on smooth and nonsmooth equations and to compare with other ones

on kicked systems modulated along the thue morse sequence we give necessary conditions for the fourier transform of the time evolution operator of kicked systems modulated along the thue morse sequence to present dirac s delta functions the case of two level systems is analysed in detail and it is found based on the trace map and numerical investigations that generically its time evolution has no quasi periodic component

expectation values of observables in time dependent quantum mechanics let u t be the evolution operator of the schrodinger equation generated by a hamiltonian of the form h0 t w t where h0 t commutes for all twith a complete set of time independent projectors p j j 1 infty consider the observable a jpj jwhere j j 0 for jlarge assuming that the matrix elements of w t behave as for p 0 large enough we prove estimates on the expectation value langle u t phi au t phi rangle equiv langle a rangle phi t for large times of the type where 0 depends on pand typical applications concern the energy expectation h0 t in case h0 t h0or the expectation of the position operator x2 t on the lattice where w t is the discrete laplacian or a variant of it and h0 t is a time dependent multiplicative potential

recurrent versus diffusive dynamics for a kicked quantum system we study the dynamics of a two level quantum system subject to a time dependent kicking perturbation modulated along the thue morse sequence for a nontrivial set of the parameters the quantum autocorrelation function is explicitly calculated and splits into a purely recurrent and a purely diffusive part furthermore the diffusive part is directly related to the singular continuous correlation measure of the thue morse sequence

extending the convergence domain of the secant and moser method in banach space we present a new semilocal convergence analysis for the secant and the moser method in order to approximate a solution of an equation in a banach space setting using the method of recurrent relations and weaker sufficient convergence criteria than in earlier studies such as amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 we increase the convergence domain of these methods the advantages are also obtained under less computational cost than in amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 numerical examples where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also provided in this study

letter to the editor frozen divided difference scheme for solving systems of nonlinear equations the development of an inverse first order divided difference operator for functions of several variables as well as a direct computation of the local order of convergence of an iterative method is presented a generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

perturbation theory of dense point spectra abstract the property of a self adjoint operator having pure point spectrum is stable under certain random compact perturbations in particular a compact perturbation of a self adjoint operator whose spectrum has lebesgue measure zero has pure point spectrum almost surely

a two step steffensen s method under modified convergence conditions a simplification of a third order iterative method is proposed the main advantage of this method is that it does not need to evaluate neither any frechet derivative nor any bilinear operator a semilocal convergence theorem in banach spaces under modified kantorovich conditions is analyzed a local convergence analysis is also performed finally some numerical results are presented

on the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum we consider quantum hamiltonians of the form h t h v t where the spectrum of h is semibounded and discrete and the eigenvalues behave as en n with 0 0 p 1 and 1 2 we show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and e is small enough more precisely for any initial condition dom h1 2 the diffusion of energy is bounded from above as h t o t where sigma alpha 2 lceil p 1 rceil gamma frac 1 2 as an application we consider the hamiltonian h t p ev t on l2 s1 d which was discussed earlier in the literature by howland

a technique to choose the most efficient method between secant method and some variants abstract a few variants of the secant method for solving nonlinear equations are analyzed and studied in order to compute the local order of convergence of these iterative methods a development of the inverse operator of the first order divided differences of a function of several variables in two points is presented using a direct symbolic computation the computational efficiency and the approximated computational order of convergence are introduced and computed choosing the most efficient method among the presented ones furthermore we give a technique in order to estimate the computational cost of any iterative method and this measure allows us to choose the most efficient among them

non stochasticity of time dependent quadratic hamiltonians and the spectra of canonical transformations the authors study the quantum mechanical evolution generated by hamiltonians which are quadratic polynomials in q and p with time dependent coefficients this evolution is determined by a unitary implementation of the phase flow of the corresponding classical hamiltonian in the case of quadratic hamiltonians which are periodic in time the floquet operator is shown to have either a pure point spectrum or a purely transient absolutely continuous spectrum thus the motion is non stochastic in a simple model of a quadratic hamiltonian with random time dependence the quantum mechanical motion is shown to be non stochastic almost surely

a proof of the dynamical version of the bombieri taylor conjecture an adaptation of the bombieri taylor conjecture on diffraction has been applied to some time dependent quantum systems here the problem is mathematically stated and a proof is presented simple examples give an idea as to what extent the conjecture is valid

convergence and numerical analysis of a family of two step steffensen s methods we provide sufficient conditions for the semilocal convergence of a family of two step steffensen s iterative methods on a banach space the main advantage of this family is that it does not need to evaluate neither any frechet derivative nor any bilinear operator but having a high speed of convergence some numerical experiments are also presented

expanding the applicability of the secant method under weaker conditions abstract we present a new semilocal convergence analysis for secant method in order to approximate a locally unique solution of a nonlinear equation in a banach space setting our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies such as amat and busquier 2003 amat et al in press argyros and hilout 2012 argyros et al 2014 argyros and magrenan 2014 2015 dennis 1971 ezquerro et al 2000 ortega and rheinboldt 1970 potra and ptak 1984 schmidt 1978 numerical examples are also presented to illustrate the theoretical results obtained in this study

some statistical properties of simple classically stochastic quantum systems numerical studies are made of simple one and two dimensional quantum models which are stochastic in the classical limit it is shown that the correlation properties of the quantum and corresponding classical motions are only similar for very short time intervals ts and that the evolution of the quantum system unlike the classical one is stable the diffusive excitation of the quantum system under a periodic perturbation is limited to a specific time interval t ts during which the diffusion rate is similar to the corresponding classical diffusion rate for the two dimensional model a continuous component in the correlation spectrum survives for an indefinite period tw t it is shown that when the perturbation is quasiperiodic the interval t increases sharply

fourier transform of a linear distribution with triangular support and its applications in electromagnetics a three dimensional fourier transform ft of a linear function with triangular support is derived in its coordinate free representation the fourier transform of this distribution is derived in three steps first the 2 d ft of a constant top hat function is obtained next the distribution is generalized to a linearly varying function finally the formulation is extended to a coordinate free representation which is the 3 d ft of the 2 d function defined over a surface this formulation is applied to the near field computation yielding accurate numerical solutions

on a steffensen s type method and its behavior for semismooth equations abstract a generalization of steffensen s method is proposed our goal is to obtain similar convergence as newton s method but without to evaluate any derivative and without to have stability problems convergence analysis and numerical results for semismooth equations are presented