analyzing the 2d fracture problems via the enriched boundary element free method in this paper the enriched boundary element free method for two dimensional fracture problems is presented an improved moving least squares imls approximation in which the orthogonal function system with a weight function is used as the basis function is used to obtain the shape functions the imls approximation has greater computational efficiency and precision than the existing moving least squares mls approximation and does not lead to an ill conditioned system of equations combining the boundary integral equation bie method and the imls approximation a boundary element free method befm for two dimensional fracture problems is obtained for two dimensional fracture problems the enriched basis function is used at the tip of the crack and then the enriched befm is presented in comparison with other existing meshless boundary integral equation methods the befm is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables and the boundary conditions can be implemented easily which leads to a greater computational precision when the enriched befm is used the singularity of the stresses at the tip of the crack can be shown better than that in the befm for the purposes of demonstration some selected numerical examples are solved using the enriched befm

relaxing convergence conditions for newton s method the classical kantorovich theorem on newton s method assumes that the first derivative of the operator involved satisfies a lipschitz condition 0 f x f y l x y in this paper we weaken this condition assuming that 0 f x f x0 x x0 for a given point x0

on the error estimates of several newton like methods1partial supported by the national natural science foundation of china and by natural science foundation of zhejiang province 1 in this paper convergence theorems and error estimates for several newton like iteration methods under new kantorovitch ostrowski type conditions using the information of higher derivatives at initial point s are established we get not only the convergence speed estimates of iterative sequence x n but also the estimates of f x n 1 f x n

a method for finding sharp error bounds for newton s method under the kantorovic assumptions this paper gives a method for finding sharpa posteriori error bounds for newton s method under the assumptions of kantorovich s theorem on the basis of this method new error bounds are derived and comparison is made among the known bounds of dennis 2 doring 4 gragg tapia 5 kantorovich 6 7 kornstaedt 9 lancaster 10 miel 11 13 moret 14 ostrowski 17 18 potra 19 and potra ptak 20

on newton s method under holder continuous derivative a mysovskii type theorem for newton s method under k p holder continuous derivative is considered in this paper for the application studied by others the new condition is weaker than ones in the literature also we prove that the optimal convergent order is p 1 for 0 p 1

boundary element free method befm for two dimensional elastodynamic analysis using laplace transform in this paper we present a direct meshless method of boundary integral equation bie known as the boundary element free method befm for two dimensional 2d elastodynamic problems that combines the bie method for 2d elastodynamics in the laplace transformed domain and the improved moving least squares imls approximation the formulae for the befm for 2d elastodynamic problems are given and the numerical procedures are also shown the befm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables and the boundary conditions can be implemented directly and easily that leads to a greater computational precision for the purpose of demonstration some selected numerical examples are solved using the befm copyright 2005 john wiley sons ltd

newton method under weak lipschitz continuous derivative in banach spaces in the present paper a relax kantorovich type condition to guarantee the convergence of newton method with order 2 in banach space is obtained which takes the well known kantorovich and smale conditions as its special cases the relations between the new condition and the old ones are also studied

geometric non linear analysis of folded plate structures by the spline strip kernel particle method this paper investigates the geometric non linear behaviour of stiffened and un stiffened folded plate structures using the spline strip kernel particle method sskpm the first order shear deformable plate theory and large deflection theory of von karman are employed the folded plate structures are considered as assemblies of individual stiffened and un stiffened flat plates that lie on different planes we regard these stiffened and un stiffened plate structures as superelements and superpose their stiffness matrices to derive the final global stiffness matrices several numerical example problems are examined and comparison studies are carried out with other available results the effect of the size of the support the order of the polynomial basis functions and the spacing of the spline nodes on the convergence of the proposed method is examined

numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms previous studies by the authors and their co workers show that the structure of equations representing shape memory alloy sma constitutive behaviour can be very similar to those of rate independent plasticity models for example the boyd lagoudas polynomial hardening model has a stress elastic strain constitutive relation that includes the transformation strain as an internal state variable a transformation function determining the onset of phase transformation and an evolution equation for the transformation strain such a structure allows techniques used in rate independent elastoplastic behaviour to be directly applicable to smas in this paper a comprehensive study on the numerical implementation of sma thermomechanical constitutive response using return mapping elastic predictor transformation corrector algorithms is presented the closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm an explicit scheme already presented in an earlier work the closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the flow rule and the inversion of the algorithmic tangent tensor a unified thermomechanical constitutive model which does not take into account reorientation of martensitic variants but unifies several of the existing sma constitutive models is used for implementation remarks on numerical accuracy of both algorithms are given and it is concluded that both algorithms are applicable for this class of sma constitutive models and preference can only be given based on the computational cost copyright 2000 john wiley sons ltd

numerical simulation of thermomechanical behaviours of shape memory alloys via a non linear mesh free galerkin formulation a new computational approach is developed based on the mesh free method for the numerical simulation of shape memory alloys a thermomechanical constitutive model is used to describe the complex material response the incremental displacement based mesh free formulation is constructed in a total lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations this mesh free formulation is not only applicable to large deformation problems but also accounts for both stress and thermally induced phase transformation moreover the newly developed mesh free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation the performance of the proposed mesh free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples copyright 2005 john wiley sons ltd

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

a new semilocal convergence theorem for newton s method abstract a new semilocal convergence theorem for newton s method is established for solving a nonlinear equation f x 0 defined in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition results on uniqueness of solution and error estimates are also given finally these results are compared with those that use kantorovich conditions

a newton type midpoint method with high efficiency index abstract in this paper we present a newton type two step method to approximate a solution of a nonlinear equation in banach spaces we establish a semilocal convergence theorem under newton kantorovich type conditions both the convergence order and the efficiency index of the developed method are found the iterative procedure presented here is a simple modification of the newton kantorovich method however with the same number of function and derivative evaluations at each iteration it is improved in two important aspects firstly the convergence order is increased from 2 for the newton kantorovich method to 1 2 2 414 for the new method secondly the efficiency index convergence order per function evaluation is improved from 2 1 414 to 1 2 1 2 1 553 we illustrate some of our results with a numerical example

on the semilocal convergence of efficient chebyshev secant type methods we introduce a three step chebyshev secant type method cstm with high efficiency index for solving nonlinear equations in a banach space setting we provide a semilocal convergence analysis for cstm using recurrence relations numerical examples validating our theoretical results are also provided in this study

two conditions concerning newton s method in this note we compare two conditions concerning newton s method and find out that even under some weaker condition one has the convergence of the newton s method and a better error bound than the relative strong condition

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

chebyshev method and convexity from convexity we obtain new convergence theorems for the chebyshev method applied to a nonlinear scalar equation f x 0 moreover kantorovich type conditions for the convergence of the chebyshev method in the complex plane are given finally a new type of assumptions are considered to prove the convergence of this method in banach spaces

on a theorem of l v kantorovich concerning newton s method we study the problem of approximating a locally unique solution of an operator equation using newton s method the well known convergence theorem of l v kantorovich involves a bound on the second frechet derivative or the lipschitz frechet differentiability of the operator involved on some neighborhood of the starting point here we provide local and semilocal convergence theorems for newton s method assuming the frechet differentiability only at a point which is a weaker assumption a numerical example is provided to show that our result can apply to solve a scalar equation where the above mentioned ones may not

a new semilocal convergence theorem for newton s method in banach space using hypotheses on the second frechet derivative a new global kantorovich type convergence theorem for newton s method in banach space is provided for approximating a solution of a nonlinear equation it is assumed that a solution exists and the second frechet derivative of the operator involved satisfies a lipschitz condition our convergence condition differs from earlier ones and therefore it has theoretical and practical value finally a simple numerical example is provided to show that our results apply where earlier ones fail

boundary element free method befm and its application to two dimensional elasticity problems in this study we first discuss the moving least square approximation mls method in some cases the mls may form an ill conditioned system of equations so that the solution cannot be correctly obtained hence in this paper we propose an improved moving least square approximation imls method in the imls method the orthogonal function system with a weight function is used as the basis function the imls has higher computational efficiency and precision than the mls and will not lead to an ill conditioned system of equations combining the boundary integral equation bie method and the imls approximation method a direct meshless bie method the boundary element free method befm for two dimensional elasticity is presented compared to other meshless bie methods befm is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables and the boundary conditions can be applied easily hence it has higher computational precision for demonstration purpose selected numerical examples are given

harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells abstract a meshfree approach the harmonic reproducing kernel particle method is proposed for the free vibration analysis of rotating cylindrical shells the reproducing kernel particle estimation is employed in hybridized form with harmonic functions to approximate the two dimensional displacement field this is the first instance in which a meshless technique has been adopted for rotating shell dynamics this technique provides ease of enforcing various types of boundary conditions and concurrently is able to capture the traveling modes the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotation are all taken into account in the present formulation this study examines in detail the effects of different boundary conditions on the frequency characteristics of rotating shells the present results wherever possible are verified by comparison against results available in the open literature in general close agreement between the authors results and those of others has been found further results presented here in selective parametric studies may be used as benchmarks for future related works

intensive structure of heisenburg supergenerator algebras over hv su2 dual carrier subspaces in liouville nmr formalisms superbosons as unit tensor superoperators abstract the structure of supergenerator algebra over simply reducible carrier space h v associated with a lie algebra over the domain of tensorial bases of nmr density operator formalisms for spin coherence are set out in terms of s 2 i s i s j s 2 j or s 2 i superbosonic forms corresponding to six unit tensors or fundamental wigner superoperators the kernel defining the characteristic null space of these unit tensors is also given some extensions of these concepts to the realm of many body nmr spin cluster problems and to rota like invariants over dual spin space are summarise the s 2 i set of component s bosons are shown to generate a group algebra and to display the requisite ladder aspects of the i set of superoperators in this respect the underlying premise yields an improved insight into the sets of su2 and su2 x s n tensors associated with nmr formalisms for spin dynamics or for model realizations of coherence transfer or relaxation by providing the intensive substructure of liouville carrier space the mapping aspects within which it has been shown that each h v is a simply reducible carrier subspace is seen as an essential preliminary aspect of su2 duality over liouville space in understanding spin cluster systems in nmr the value of p kq s 2 i monomial formalisms in appreciating the structure of liouville space and its associated transformational properties is stressed

extending the newton kantorovich hypothesis for solving equations the famous newton kantorovich hypothesis kantorovich and akilov 1982 3 argyros 2007 2 argyros and hilout 2009 7 has been used for a long time as a sufficient condition for the convergence of newton s method to a solution of an equation in connection with the lipschitz continuity of the frechet derivative of the operator involved here using lipschitz and center lipschitz conditions and our new idea of recurrent functions we show that the newton kantorovich hypothesis can be weakened under the same information moreover the error bounds are tighter than the corresponding ones given by the dominating newton kantorovich theorem argyros 1998 1 2 7 ezquerro and hernandez 2002 11 3 proinov 2009 2010 16 17 numerical examples including a nonlinear integral equation of chandrasekhar type chandrasekhar 1960 9 as well as a two boundary value problem with a green s kernel argyros 2007 2 are also provided in this study

a new semilocal convergence theorem for newton s method involving twice frechet differentiability at only one point in this study we provide a new semilocal convergence theorem for newton s method it is assumed that an operator is twice continuously frechet differentiable at only one point finally a simple numerical example is given to show that our results can apply but earlier similar ones fail

contrasting routes to the kostka coefficients of λ boxvr n ln permutational module expansions for 6 n 8 applications to nmr spin clusters under su m n ln spin symmetries abstract aspects of the higher n l n permutational modules associated with young subgroups of various highly branched high n fold algebras which are pertinent to identical spin nmr clusters are presented for boxvr n or boxvr n arota p tuple or number partition the method of optimal choice for deriving the kostka coefficients found in sets derived from permutational module expansions rests on the ordering of the shape to the self associated diagram s in the dominance hierarchy hence physical insight into these cage cluster nmr systems is developed both from these properties and from the inter related induced symmetries of gl n and l n groups from these associated combinatorial mapping or scalar invariant aspects of su m n l n symmetry one may define the a n l n systems of ax n nmr problems in a general semi topological limit this corresponds to a high n l n limit in which the individual spin cluster exhibits a lack of any intracluster magnetic equivalence properties

the convergence ball of newton s method and the uniqueness ball of equations under holder type continuous derivatives abstract under the hypotheses that nonlinear operators have k p holder type continuous derivatives exact estimates of the radius of the convergence ball of newton s method and of the uniqueness ball of solution of equations are obtained

starting points for newton s method under a center lipschitz condition for the second derivative abstract we analyze the semilocal convergence of newton s method under a center lipschitz condition for the second derivative of the operator involved different from that used by other authors until now in particular we propose to center the lipschitz condition for the second derivative in a different point from that where newton s method starts this allows us to obtain different starting points for newton s method and modify the domain of starting points

kantorovich s type theorems for systems of equations with constant rank derivatives the famous newton kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of newton s method to a solution of an equation here we present a kantorovich type convergence analysis for the gauss newton s method which improves the result in w m hauszler a kantorovich type convergence analysis for the gauss newton method numer math 48 1986 119 125 and extends the main theorem in i k argyros on the newton kantorovich hypothesis for solving equations j comput appl math 169 2004 315 332 furthermore the radius of convergence ball is also obtained

on the secant method for solving nonsmooth equations in this study we are concerned with the problem of approximating a locally unique solution of an operator equation in banach space using the secant method the differentiability of the operator involved is not assumed using a flexible point based approximation we provide a local as well as a semilocal convergence analysis for the secant method our results are justified by numerical examples that cannot be handled with earlier works

convergence criterion of newton s method for singular systems with constant rank derivatives abstract the present paper is concerned with the convergence problem of newton s method to solve singular systems of equations with constant rank derivatives under the hypothesis that the derivatives satisfy a type of weak lipschitz condition a convergence criterion based on the information around the initial point is established for newton s method for singular systems of equations with constant rank derivatives applications to two special and important cases the classical lipschitz condition and the smale s assumption are provided the latter in particular extends and improves the corresponding result due to dedieu and kim in j p dedieu m kim newton s method for analytic systems of equations with constant rank derivatives j complexity 18 2002 187 209

extending the domain of starting points for newton s method under conditions on the second derivative abstract in this paper we propose a center lipschitz condition for the second frechet derivative together with the use of restricted domains in order to improve the domain of starting points for newton s method in addition we compare the new result with an older one and see that the former improves the latter

a modification of the classical kantorovich conditions for newton s method in the classical kantorovich theorem on newton s method it is assumed that the second frechet derivative of the involved operator satisfies the condition f x k in an appropiate domain in this paper we study a modification of this condition assuming that f x x where is a continuous and non decreasing real function

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

indices of convexity and concavity application to halley method we define an index to measure the convexity of a convex function f at each point we use this index to establish conditions on the convergence of the halley method in the complex plane and in banach spaces

a note on the kantorovich theorem for newton iteration abstract in this paper a new theorem for the newton method convergence is obtained its condition is different from that of the kantorovich theorem and therefore it has theoretical and practical value

specialised nmr spin cluster symmetry chains under su m x ln group dualities role of democratic recoupling and projective geometric mapping from su m p tuples onto γ γ v ln or onto γ v ln g for 6 n fold cage clusters the inherent nature of the dual group spin algebras for nmr spin clusters over their associated carrier spaces is examined in the context of scalar invariants sis the a n su m ln g aspects of ax n cage spin biclusters furnish these si forms and focus our attention on their part in the ln induced representational hierarchy for democratic recoupling in nmr spin dynamical formalisms the purpose of the present work is to examine the nature of the specialised symmetry chains their mappings and su2 distinct hv carrier subspaces especially for non magnetically equivalent non me supermolecular spin biclusters in the 6 n 20 60 2160 limit a hierarchy of intracluster jij interactions ensures that the ln group and its graph theoretical schemata dominate the spin algebra these heisenberg aspects arise from the bilinear terms of the zeroth hamiltonian 0 their dominance highlights certain contrasts with conventional unitary algebras and wigner unit operator properties the explicit induced symmetry recoupling labels over su2 ln carrier subspaces of cluster liouville nmr formalisms temme physica a 166 1990 676 198 1993 245 allow a stepwise subduction over the dual symmetry chain from rota scalar invariants over a field or p tuples number parts of n r r r r as su m within the chain su m v ln v ln g as demonstrated e g for 6 n 12 20 60 2160 and m 3 4 6 spin systems of bh 2 n 13ch 20 or 13cf n as as member of the set of n 60z2 supermolecular fullerenes for the dodecahedral spin symmetries of projective geometric aspects of high p m m2 tuples yield further detailed insight into the nature of group duality over spin algebras of both hilbert and liouville spaces such views go beyond the physical insight derivable from the study of casimir invariants whose proper role lies elsewhere the dual symmetry chain and mapping concepts presented here are placed in the context both of graph theory of nmr spin clusters k balasubramanian j chem phys 78 1982 6369 and of some recent views on augmented boson algebras referred to above

local convergence of inexact newton like iterative methods and applications abstract we provide local convergence results in affine form for inexact newton like as well as quasi newton iterative methods in a banach space setting we use hypotheses on the second or on the first and second frechet derivative of the operator involved our results allow a wider choice of starting points since our radius of convergence can be larger than the corresponding one given in earlier results using hypotheses on the first frechet derivative only a numerical example is provided to illustrate this fact our results apply when the method is for example a difference newton like or update newton method furthermore our results have direct applications to the solution of autonomous differential equations

a newton kantorvich theorem for equations involving m frechet differentiable operators and applications in radiative transfer abstract in this study we approximate a locally unique solution of a nonlinear operator equation in banach space using newton s method a complete error analysis showing the quadratic convergence of our method is also given our new theorem uses lipschitz or holder continuity assumptions on m frechet differentiable operators where m 2 is a positive integer a numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results a second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer

casimir operators duality and the point groups in atomic or nuclear shell theory the quadratic casimir operators can be used to evaluate the expectation values of two body interactions among equivalent members of a shell racah has given closed expressions for these casimir operators for all the groups in the racah chain in this paper an alternate derivation of these closed expressions based on duality with the symmetric group is given the derivation allows extension of these expressions to situations in which equivalent spins are in an environment such as a point group for which the two body interactions separate into distinct sets possible application to nmr systems with spin 1 2 are discussed

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

solving nonlinear equations system via an efficient genetic algorithm with symmetric and harmonious individuals we present an efficient genetic algorithm as a general tool for solving optimum problems as a specialized application this algorithm can be used to approximate a solution of a system of nonlinear equations on n dimensional euclidean space setting the new idea involves the introduction of some pairs of symmetric and harmonious individuals for the generation of a genetic algorithm the population diversity is maintained better this way the elitist model is used to ensure the convergence simulation results show that the new method is indeed very effective

third order convergence theorem by using majorizing function for a modified newton method in banach space abstract following the ideas of frontini and sormani we present a modified newton method in banach space which is used to solve the nonlinear operator equation we establish the newton kantorovich convergence theorem for the modified newton method with third order convergence in banach space by using majorizing function we also get the error estimate finally two examples are provided to show the application of our theorem

weak convergence conditions for inexact newton type methods abstract we establish a new semilocal convergence results for inexact newton type methods for approximating a locally unique solution of a nonlinear equation in a banach spaces setting we show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works 15 31 special cases and numerical examples are also provided in this study

on newton s method for solving equations containing frechet differentiable operators of order at least two we provide sufficient conditions for the semilocal convergence of newton s method to a locally unique solution of a nonlinear operator equation containing operators that are frechet differentiable of order at least two in a banach space setting numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot j m gutierrez a new semilocal convergence theorem for newton s method j comput appl math 79 1997 131 145 z huang a note of kantorovich theorem for newton iteration j comput appl math 47 1993 211 217 f a potra sharp error bounds for a class of newton like methods libertas mathematica 5 1985 71 84

a steffensen s type method in banach spaces with applications on boundary value problems in this paper a modified steffensen s type iterative scheme for the numerical solution of a system of nonlinear equations is studied two convergence theorems are presented the numerical solution of boundary value problems by the multiple shooting method using the proposed iterative scheme is analyzed

extending the applicability of newton s method for k frechet differentiable operators in banach spaces we extend the applicability of newton s method for k frechet differentiable operators in a banach space setting by using a more flexible way of computing upper bounds on the inverses of the operators involved in particular we improve and extend the recent works by ezquerro et al 2012 2013 13 15 moreover we illustrate our study with some numerical examples involving hammerstein integral equations

computational aspects of one dimensional shape memory alloy modeling with phase diagrams abstract a constitutive model for martensitic solid solid phase transformations is developed specifically we investigate and model the one dimensional behavior of shape memory alloys with the purpose of capturing both the shape memory effect and the pseudoelasticity effect which are uniquely exhibited by this class of alloys the model is of the popular phase space type and an appropriate numerical approximation of the constitution is developed which robustly handles arbitrary one dimensional thermomechanical loading heuristics are provided for treating two types of non uniqueness issues that have been identified to arise with such models representative simulations demonstrate the ability of the formulation to capture the essential macroscopic behavior of shape memory alloys in particular examples are shown solving truss bar and beam finite element problems

weak convergence conditions for the newton s method in banach space using general majorizing sequences using the majorizing principle we develop sufficient convergence conditions for the semilocal convergence of newton s method in a banach space setting the involved majorizing sequences are very general and as special cases include most relevant sequences from the published literature our convergence conditions can be weaker and our error analysis can be finer than before

on the local convergence of fast two step newton like methods for solving nonlinear equations a local convergence analysis is presented for a fast two step newton like method tsnlm for solving nonlinear equations in a banach space setting the tsnlm unifies earlier methods such as newton s secant newton like chebyshev secant chebyshev newton steffensen stirling s and other single or multistep methods numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper

finite element analysis of the behavior of shape memory alloys and their applications abstract a nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy material behavior the constitutive equations include the necessary internal variables to account for the material transformations and are utilized in a one dimensional finite element procedure that captures the unique shape memory alloy responses of pseudoelasticity and of the shape memory effect at all temperatures stress levels and loading conditions detailed material properties for the alloy used are necessary for the analysis the solution of the geometrically and physically nonlinear problem is achieved by application of a newton s method in which a sequence of linear problems is numerically solved due to consistent linearization a quadratic rate of convergence is obtained several test cases are presented to illustrate the potential of the finite element procedure cases simulating the stress strain behavior of a bar of shape memory alloy under simple uniaxial loading as well as restrained recovery responses at different temperatures compare well with experimental and analytical results two further generalized applications are examined the use of a shape memory alloy ring as a pipe connector and eigenfrequency tuning of a composite beam with embedded shape memory wires the results of these analyses correlate well with analytical results and the methodology for use of the finite element procedure in general cases is demonstrated the finite element procedure is thus shown to be a powerful tool for studying various applications of shape memory alloys

a new convergence theorem for the jarratt method in banach space abstract in this study we approximate a locally unique solution of a nonlinear equation in banach space using the jarratt method sufficient convergence conditions for this method have already been given by several authors when the equation is defined on the real line or complex plane 1 3 or in banach space 1 4 7 if a certain newton kantorovich type hypothesis is satisfied then the jarratt method converges to a solution of the equation with order four the verification of some of the earlier hypotheses is too difficult or too expensive here using lipschitz conditions on the second frechet derivative of the operator involved we provide a convergence theorem for the jarratt method which uses conditions that are very easy to check see the example and remark 4 finally a numerical example is provided to show that our results apply to solve a nonlinear equation where others fail

majorizing functions and two point newton type methods the semi local convergence of a newton type method used to solve nonlinear equations in a banach space is studied we also give as two important applications convergence analyses of two classes of two point newton type methods including a method mentioned in 5 and the midpoint method studied in 1 2 12 recently interest has been shown in such methods 3 4

a uniparametric family of iterative processes for solving nondifferentiable equations in this work we study a class of secant like iterations for solving nonlinear equations in banach spaces we consider a condition for divided differences which generalizes the usual ones i e lipschitz and holder continuous conditions a semilocal convergence result is obtained for nondifferentiable operators for that we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution finally we apply our results to the numerical solution of several examples