on the method of tangent hyperbolas on banach spaces abstract as an application of the technique employed by the author in a series of papers 15 18 some results are established concerning convergence of the method of tangent hyperbolas for solving nonlinear equations in banach spaces as well as existence and uniqueness of solution the results are compared with those obtained by doring 5

a newton kantorovich convergence theorem for the inverse free jarratt method in banach space abstract under the weaken conditions we establish the newton kantorovich convergence theorem of inverse free jarratt method in banach space which is used to solve the nonlinear operator equation finally some examples are provided to show the application of our theorem

ergodicity of the 2d navier stokes equations with degenerate stochastic forcing the stochastic 2d navier stokes equations on the torus driven by degenerate noise are studied we characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic in particular our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in l 2 0 t 2 unlike previous works this class is independent of the viscosity and the strength of the noise the two main tools of our analysis are the asymptotic strong feller property introduced in this work and an approximate integration by parts formula the first when combined with a weak type of irreducibility is shown to ensure that the dynamics is ergodic the second is used to show that the first holds un

application of iterative processes of r order at least three to operators with unbounded second derivative abstract in this paper we apply a family of newton like methods which contains the best known iterative processes to operator equations where the usual convergence conditions are relaxed we weaken these conditions by assuming f x0 and f x f y x y with a non decreasing continuous real function our results include the ones obtained when the convergence of the family is studied under lipschitz continuous or holder continuous conditions for the second derivative of the operator involved to finish we apply the study to boundary value problems

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

random attractors for stochastic 2d navier stokes equations in some unbounded domains abstract we show that the stochastic flow generated by the 2 dimensional stochastic navier stokes equations with rough noise on a poincare like domain has a unique random attractor one of the technical problems associated with the rough noise is overcomed by the use of the corresponding cameron martin or reproducing kernel hilbert space our results complement the result by brze niak and li 2006 10 who showed that the corresponding flow is asymptotically compact and also generalize caraballo et al 2006 12 who proved existence of a unique attractor for the time dependent deterministic navier stokes equations

a moderate deviation principle for 2 d stochastic navier stokes equations in this paper we prove a central limit theorem and establish a moderate deviation principle for twodimensional stochastic navier stokes equations with multiplicative noise the weak convergence method plays an important role

analysis of time fractional and space nonlocal stochastic incompressible navier stokes equation driven by white noise abstract in this paper we consider the stochastic time space fractional incompressible navier stokes equation driven by white noise we firstly derive the regularity of the nonlocal stochastic convolution then we prove the global existence and uniqueness of the mild solution finally the holder continuity for the stochastic time space fractional incompressible navier stokes equation driven by white noise is established the optimal holder continuity accords with the result of integer order time incompressible navier stokes equation

a special matrix equation and its application in microelectronics abstract a special matrix equation is examined which arises in designing electrical interconnections between microelectronic circuits and systems the equation is first rewritten as a fixed point problem a globally convergent iteration method is then proposed and monotone convergence is proved a sufficient and necessary condition for the existence of the solution is presented the solution can be used to minimize the reflection coefficients of the active signals

stochastic navier stokes equations with caputo derivative driven by fractional noises abstract in this paper we consider the extended stochastic navier stokes equations with caputo derivative driven by fractional brownian motion we firstly derive the pathwise spatial and temporal regularity of the generalized ornstein uhlenbeck process then we discuss the existence uniqueness and holder regularity of mild solutions to the given problem under certain sufficient conditions which depend on the fractional order and hurst parameter h the results obtained in this study improve some results in existing literature

a note on the halley method in banach spaces abstract we provide a convergence theorem under the usual ostrowski kantorovich conditions for an equivalent form of the halley method in banach spaces the best possible upper error bound for the method is obtained some applications to the solution of quadratic operator equations are provided

results on newton methods part i a unified approach for constructing perturbed newton like methods in banach spaces and their applications many applied problems can be formulated to fit the model of a nonlinear equation undoubtedly newton methods are the most popular methods for solving such equations here we report the results of our recent investigations in a series of two papers we unified newton methods and provided convergence results to solve nonlinear equations we used newton kantorovich type hypotheses and the majorant method our results depend on the existence of a lipschitz function with which we replace the lipschitz constant usually appearing in the hypotheses of these investigations we find our methods useful for many reasons from the computational point of view we have allowed our iterations to be corrected at every step and still converge to a solution of the equation at hand in most earlier results the iterates are assumed to be computed exactly to achieve convergence moreover we showed that under weaker hypotheses our iterations converge faster than others already in the literature finally we used our results to solve uryson and fredholm type integral equations appearing in radiative transfer

modified chebyshev halley methods with sixth order convergence abstract in this paper we present a family of modified chebyshev halley methods the new methods add one evaluation of the function at the point iterated by chebyshev halley methods analysis of convergence shows that these methods have sixth order convergence numerical results show that the new methods can be of practical interest

dynamic response of a double euler bernoulli beam due to a moving constant load in this paper the dynamic response of a double beam system traversed by a constant moving load is studied the system consists of two elastic homogeneous isotropic euler bernoulli beams the two simply supported prismatic beams are identical parallel one upon the other and connected continuously by a viscoelastic layer the dynamic deflections of both beams are given in analytical closed forms the effects of the moving speed of the load and the damping and the elasticity of the viscoelastic layer on the dynamic responses of the beams are investigated in detail also several plots of the deflections of the beams are given and discussed for different values of speed parameter damping ratio and stiffness parameter furthermore the force transmitted between the beams is determined and the effects of the system parameters on this force are studied plots of the maximum responses of the beams are presented

on the time fractional navier stokes equations abstract this paper is concerned with the navier stokes equations with time fractional derivative of order 0 1 this type of equations can be used to simulate anomalous diffusion in fractal media we establish the existence and uniqueness of local and global mild solutions in h q meanwhile we also give local mild solutions in j q moreover we prove the existence and regularity of classical solutions for such equations in j q

modelling of floating slab tracks with continuous slabs under oscillating moving loads this paper discusses modelling of floating slab tracks on rigid foundations the model consists of an upper euler bernoulli beam to account for both the rails and a lower euler bernoulli beam to account for the slab there are two continuous resilient layers in the model one to account for railpads between the rails and the slab and one to account for slab bearings underneath the slab the fourier transformation method is used to calculate displacements of such a track under an oscillating moving load these results are used to calculate the cut on frequencies and critical velocity of the track the work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves critical velocities load velocity lines and coupling of systems in the wavenumber frequency domain the paper offers a complete treatment of the issues important to the analysis of a double beam system not elsewhere available in the published literature

the secant method in generalized banach spaces we provide convergence results and error estimates for the secant method in generalized banach spaces the idea of a generalized norm is used which is defined to be a map from a linear space into a partially ordered banach space convergence results and error estimates are improved over the real norm theory

the improvements of chebyshev halley methods with fifth order convergence abstract in this paper we present a family of new fifth order methods which improves the classical chebyshev halley methods with cubic convergence the new methods add one evaluation of the function at the point iterated by chebyshev halley methods analysis of efficiency shows that the new methods can be of practical interest which is also corroborated by numerical tests

the existence of energy solutions to 2 dimensional non lipschitz stochastic navier stokes equations in unbounded domains in this paper we consider the existence and uniqueness of weak energy solutions to a stochastic 2 dimensional non lipschitz navier stokes equation perturbed by the cylindrical wiener process w t in a bounded or unbounded domain d with the smooth boundary d or d r2 dx t ax t b x t dt f t x t dt g t x t dw t where a is the stokes operator and f g satisfy the non lipschitz condition

mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

large deviation principles for 2 d stochastic navier stokes equations driven by levy processes abstract in this paper we establish a large deviation principle for the two dimensional stochastic navier stokes equations driven by levy processes which involves the study of the levy noise and the investigation of the effect of the highly nonlinear unbounded drifts

on the convergence of a certain class of iterative procedures under relaxed conditions with applications we provide sufficient convergence conditions for a certain class of inexact newton like methods to a locally unique solution of a nonlinear equation in a banach space the equation contains a nondifferentiable term and at each step we use the inverse of the same linear operator we use ptak like conditions that are weaker than earlier ones our results apply whenever earlier ones do but not vice versa a semilocal convergence result is also given based on the contraction mapping principle finally our results apply to solve a nonlinear integral equation of uryson type appearing in elasticity theory that cannot be solved with existing methods

on the convergence of two step methods generated by point to point operators in this study we examine conditions for the convergence of two step methods generated by point to point operators iterations of this type have a great importance in optimization theory stability analysis of dynamic systems and many other fields of applied mathematics the speed of convergence is also examined using the theory of majorants in a banach space setting the monotone convergence of these methods is also examined in a partially ordered topological space special cases of our results reduce to corresponding results already in the literature in particular relevant work can be found in i k argyros appl math comput 61 1 1994 51 69 and f szidarovasky and o palusinski appl math comput 64 1994 115 119 and references therein some applications are also given to the solution of systems of nonlinear integral equations of uryson type

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

sufficient conditions for constructing methods faster than newton s in this study we use inexact newton like methods to approximate a locally unique solution of a nonlinear operator equation in a banach space using the majorant method and newton kantorovich type hypotheses we provide sufficient convergence conditions and an error analysis for our method our method is also shown under very natural assumptions to be faster than newton s under the same computational cost finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant flux emerging from a plane radiation field

forced transverse vibrations of an elastically connected complex rectangular simply supported double plate system abstract the paper deals with forced transverse vibrations of an elastically connected rectangular double plate system this complex continuous system can represent a certain simplified model of a three layered structure consisting of two parallel thin plates separated by an elastic massless layer of a winkler type undamped motion of the system excited by arbitrarily distributed continuous loadings subjected transversely to both plates are governed by a linear set of two coupled non homogeneous partial differential equations based on the kirchhoff love plate theory the forced vibration problem is solved generally by the application of the modal expansion method in the case of simply supported boundary conditions for plates on the basis of general solutions obtained three particular cases of the action of exciting stationary harmonic loads are considered an analysis of harmonic responses of the system makes it possible to determine conditions of resonance and dynamic vibration absorption a numerical example is given to illustrate the theory presented

on the monotone convergence of algorithmic models in this paper we provide first monotone convergence conditions for general algorithmic models practical conditions for linear spaces are then derived from the general theory in particular our results can apply to show monotone convergence of newton like methods

vibration of a double beam system abstract an exact method is presented for solving the vibration of a double beam system subject to harmonic excitation the system consists of a main beam with an applied force and an auxiliary beam with a distributed spring k and dashpot c in parallel between the two beams the viscous damping and the applied forcing function can be completely arbitrary the damping is assumed to be neither small nor proportional and the forcing function can be either concentrated at any point or distributed the euler bernoulli model is used for the transverse vibrations of beams and the spring dashpot represents a simplified model of viscoelastic material the method involves a simple change of variables and modal analysis to decouple and to solve the governing differential equations respectively a case study is solved in detail to demonstrate the methodology and the frequency responses are shown in dimensionless parameters for low and high values of stiffness k k0 and damping c c0 the plots show that each natural mode consists of two submodes 1 the in phase submode whose natural frequencies and resonant peaks are independent of stiffness and damping and 2 the out of phase submode whose natural frequencies are increased with increasing stiffness and resonant peaks are decreased with increasing damping the closed form solution and the plots especially the three dimensional ones not only illustrate the principles of the vibration problem but also shed light on practical applications

third order iterative methods for operators with bounded second derivative abstract we analyse the classical third order methods chebyshev halley super halley to solve a nonlnnear equation f x 0 where f is an operator defined between two banach spaces until now the convergence of these methods is established assuming that the second derivative f satisfies a lipschitz condition in this paper we prove by using recurrence relations the convergence of these and other third order methods just assuming f is bounded we show examples where our conditions are fulfilled and the classical ones fail

free transverse vibrations of an elastically connected complex beam string system abstract the present work is devoted to theoretical vibration analysis of a complex mixed continuous system undamped free transverse vibrations of an elastically connected beam string system are considered solutions of the problem are formulated by using the modal expansion method two infinite sequences of the natural frequencies corresponding to two possible kinds of vibration motions synchronous and asynchronous are determined in a numerical example illustrating the theory presented the effect of string tension force on the natural frequencies of the system is investigated in detail

stochastic generalized burgers equations driven by fractional noises abstract the existence and uniqueness are proved for the solutions to a class of stochastic generalized burgers equations driven by multi parameter fractional noises in addition the existence and moment estimate are also obtained for the density of such a solution

a galerkin finite element method for time fractional stochastic heat equation abstract in this study a galerkin finite element method is presented for time fractional stochastic heat equation driven by multiplicative noise which arises from the consideration of heat transport in porous media with thermal memory with random effects the spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained numerical techniques are developed by the standard galerkin finite element method in spatial direction and gorenflo mainardi moretti paradisi scheme is applied in temporal direction the convergence error estimates for both semi discrete and fully discrete schemes are established finally numerical example is provided to verify the theoretical results

convergence rates for inexact newton like methods at singular points and applications newton s method converges linearly rather than quadratically if the initial guess is close to the solution and the frechet derivative is singular at the solution several authors have already tried to improve the rate of convergence for this method in this case the limitations of their approach is twofold first the residuals at each step are assumed to be zero which is not the case in general second the previous works are limited only to the ordinary newton method here we extend and improve on these results by providing convergence rates for inexact newton like methods on a banach space setting moreover our results reduce to the ones already in the literature for special choices of the operators involved we complete our study with some numerical examples appearing in connection with some predator prey problems appearing in population modeling that show how our results improve on the earlier ones

free vibrations of elastically connected stretched beams abstract a general theory for the determination of natural frequencies and mode shapes for a set of elastically connected axially loaded euler bernoulli beams is developed a normal mode solution is applied to a set of non dimensional coupled partial differential equations the natural frequencies are the eigenvalues of a matrix of differential operators the matrix operator is shown to be self adjoint leading to an orthogonality condition for the mode shapes in the special case of identical beams it is shown that the natural frequencies are organized into sets of intramodal frequencies in which each mode shape is a product of a spatial mode and a discrete mode an exact solution is available for the general case however the natural frequencies and mode shapes are then determined using a complicated numerical method a rayleigh ritz method using mode shapes of the corresponding unstretched beams is developed as an alternative

global l2 solutions of stochastic navier stokes equations this paper concerns the cauchy problem in r d for the stochastic navier stokes equation 1 u u u u p f u u p g u o w u 0 u 0 div u 0 driven by white noise w under minimal assumptions on regularity of the coefficients and random forces the existence of a global weak martingale solution of the stochastic navier stokes equation is proved in the two dimensional case the existence and pathwise uniqueness of a global strong solution is shown a wiener chaos based criterion for the existence and uniqueness of a strong global solution of the navier stokes equations is established

a uniparametric chebyshev type method free from second derivatives in this paper we present a family of new chebyshev type methods free from second derivatives for solving non linear equations analysis of convergence shows that these new methods are cubically convergent as particular cases we introduce two efficient methods in this family of the new methods the practical utility of which is demonstrated by numerical examples

new modified multi level residue harmonic balance method for solving nonlinearly vibrating double beam problem abstract in this study a new modified multi level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams although numerous nonlinear beam or linear double beam problems have been tackled and solved there have been few studies of this nonlinear double beam problem the geometric nonlinear formulations for a double beam model are developed the main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level this heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method the proposed method can generate the higher level nonlinear solutions that are neglected by the previous modified harmonic balance method the results from the proposed method agree reasonably well with those from the classical harmonic balance method the effects of damping axial force and excitation magnitude on the nonlinear vibrational behaviour are examined

damped vibration analysis of an elastically connected complex double string system abstract the main purpose of the present paper is to consider theoretically damped transverse vibrations of an elastically connected double string system this system is treated as two viscoelastic strings with a kelvin voigt viscoelastic layer between them a theoretical analysis has been made for a simplified model of the system in which assumed physical parameters make it possible to decouple the governing equations of motion by introducing the principal co ordinates applying the method of separation of variables and the modal expansion method exact analytical solutions for damped free and forced responses of the system subjected to arbitrarily distributed transverse continuous loads are determined in the case of arbitrary magnitude of linear viscous damping it is important to note that the solutions obtained are explicitly expressed in terms of parameters characterizing the physical properties of the system under discussion for the sake of completeness of the analysis solutions for undamped free and forced vibrations are also formulated

time space fractional stochastic ginzburg landau equation driven by fractional brownian motion abstract the current paper is devoted to the time space fractional ginzburg landau equation driven by fractional brownian motion the spatial temporal regularity of the nonlocal stochastic convolution is firstly established and then the existence and uniqueness of the global mild solution are obtained by the banach fixed point theorem and mittag leffler functions finally the numerical simulations for the time fractional stochastic ginzburg landau equation are provided to verify the mathematical analysis results

chebyshev halley s method on riemannian manifolds abstract this paper is concerned with the problem of finding singular points of vector fields on riemannian manifolds we using non trivial techniques and results of differential geometry will exhibit a new method defined on complete riemannian manifolds which generalizes the important newton and chebyshev halley s methods moreover a characterization of the convergence under kantorovich type conditions and error estimates are also given in this study using the method introduced in this paper we give an algorithm which will allow us to find singular points of a vector field on the two dimensional sphere s 2 finally in order to illustrate our method and its relevance we develop an example which allows us to find a singularity of a vector field on s 2 such a singularity is not possible to find it using the classical numerical methods on r 3

stochastic burgers equation with fractional derivative driven by multiplicative noise abstract this article is devoted to the study of the existence and uniqueness of mild solution to time and space fractional stochastic burgers equation perturbed by multiplicative white noise the required results are obtained by stochastic analysis techniques fractional calculus and semigroup theory moreover we prove the regularity properties of mild solution to this generalized burgers equation in the framework of bochner spaces

weak solutions of the time fractional navier stokes equations and optimal control abstract in this paper we deal with the navier stokes equations with the time fractional derivative of order 0 1 which can be used to simulate anomalous diffusion in fractal media we firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of galerkin approximations in the case that the dimension n 4 moreover a complete proof of the uniqueness is given when n 2 at last we give a sufficient condition of optimal control pairs

ergodicity of the 2 d navier stokes equation under random perturbations a 2 dimensional navier stokes equation perturbed by a sufficiently distributed white noise is considered existence of invariant measures is known from previous works the aim is to prove uniqueness of the invariant measures strong law of large numbers and convergence to equilibrium

two dimensional navier stokes equations driven by a space time white noise abstract we study the two dimensional navier stokes equations with periodic boundary conditions perturbed by a space time white noise it is shown that although the solution is not expected to be smooth the nonlinear term can be defined without changing the equation we first construct a stationary martingale solution then we prove that for almost every initial data with respect to a measure supported by negative spaces there exists a unique global solution in the strong probabilistic sense

vibrations of double string complex system under moving forces closed solutions in this paper the dynamic response of a double string system traversed by a constant or a harmonically oscillating moving force is considered the force is moving with a constant velocity on the top string the strings are identical parallel one upon the other and continuously coupled by a linear winkler elastic element the classical solution of the response of a double string system subjected to a force moving with a constant velocity has a form of an infinite series the main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed analytical form instead of an infinite series the presented method of finding the solution in a closed analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations

stochastic burgers equation driven by fractional brownian motion abstract in this paper we consider the stochastic burgers equation driven by a genuine cylindrical fractional brownian motion with hurst parameter h 1 4 we first prove the regularities of the solution to the linear stochastic problem corresponding to the stochastic burgers equation then we obtain the local and global existence and uniqueness results for the stochastic burgers equation

on a family of second derivative free variants of chebyshev s method in this paper we present a family of new second derivative free variants of chebyshev s method in which f x 0 in some points is permitted analysis of convergence shows that the new methods are cubically convergent analysis of efficiency in term of function evaluations shows that the new methods have the great practical utility which is demonstrated by numerical examples