performance comparison of numerical inversion methods for laplace and hankel integral transforms in engineering problems abstract different methods for the numerical evaluations of the inverse laplace and inverse of joint laplace hankel integral transforms are applied to solve a wide range of initial boundary value problems often arising in engineering and applied mathematics the aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half space to concentrated impulse or those related to viscoelastic wave motion in layered media these classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations theoretical seismology soil structure interaction in time domain and so on therefore their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems some different methods are also investigated in detail and compared for the inversion of the joint hankel laplace transforms where more sophisticated integrand functions are encountered it is shown that durbin crump d amore fixed talbot gaver whyn rho gwr and direct integration methods have excellent performance and produce good results when applied to the same problems on the contrary gaver stehfest and piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for simple transformed functions particularly the performance of gwr algorithm is very good even for transformed functions with infinite number of singularities where the other methods fail in addition in case of double integral transforms only the fixed talbot durbin and weeks methods are recommended

numerical simulation for non linear thermal wave the present work applies the hybrid method of the laplace transform technique and a modified discretization scheme to analyze the non linear hyperbolic heat conduction problems in a semi infinite domain with either linearly or exponentially temperature dependent thermal conductivity the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the transformed equations are discretized by a modified discretization scheme to show the rationality and reliability of the present results a comparison between the present numerical results and those in the literature is made results show the behavior of hyperbolic heat conduction is sensitive to the function form of thermal conductivity the speed of heat propagation changes for the variation of thermal conductivity

disturbance due to mechanical sources in micropolar elastic medium with voids the dynamic response of a homogeneous isotropic micropolar half space with voids subjected to a set of normal point sources is investigated the integral transforms have been inverted by using a numerical technique to obtain the normal force stress normal displacement tangential force stress tangential couple stress and volume fraction field in the physical domain for the two different sources the results of these quantities for a magnesium crystal like material are given and illustrated

boundary integral equation method for linear porous elasticity with applications to soil consolidation for physical phenomena governed by the biot model of porous elasticity a reciprocal relation similar to the betti s recoprocal theorem in elasticity is constructed in laplace transformed space integrating the reciprocal relation enables one to formulate boundary integral equations the fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material numerical implementation of two dimensional problems includes finite element ideas of discretization and polynomial interpolation and numerical inversion of a laplace transform practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids also as a numerical experiment consolidation of partially saturated soil is simulated and interesting phenomena are observed the currently developed boundary integral equation method biem for porous elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods for linear consolidation problems application of biem is always preferred to the other numerical methods whenever possible

periodically varying heat source response in a functionally graded microelongated medium abstract the present paper deals with the response due to periodically varying heat sources in the neighborhood of the origin of a functionally graded isotropic unbounded microelongated medium in the context of generalized thermoelastic theory the expressions for displacement microelongation and temperature fields have been obtained in laplace fourier transformed domain after computing the inverse fourier transforms by contour integration technique the inversion of laplace transforms has been obtained numerically the changes of displacement microelongation and normal strain have been shown graphically for different types of heat source

study of non fickian diffusion problems with the potential field in the cylindrical co ordinate system the present study applies a hybrid numerical scheme of the laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one dimensional non fickian diffusion problems in the cylindrical co ordinate system the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the resulting equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem the strength of the jump discontinuity can be reduced by increasing the value of the potential gradient the propagation speed of mass wave is independent of the potential gradient and the boundary condition copyright 2003 john wiley sons ltd

behavior of micropolar cubic crystal due to various sources the response of a micropolar cubic crystal due to various sources acting at the free surface has been studied the eigenvalue approach using integral transforms has been employed and the transforms have been inverted by using a numerical technique the displacement stress and microrotation components in the physical domain are obtained numerically the results of displacement and stresses have been compared for micropolar cubic crystal and micropolar isotropic solid the numerical results are illustrated graphically for a particular model

improvement of accuracy in numerical methods for inverting laplace transforms based on the post widder formula abstract the paper proposes a new computational version for numerical inversion of laplace transforms at a point and on an interval based on the post widder formula in this version the original sequence of post widder approximants is calculated using operations on series and the approximate value of the sought function is constructed as a limit of this sequence using polynomial and rational extrapolation to the limit some procedures are proposed for improvement of accuracy in the problem of inversion at equidistant points of an interval without computing additional approximants an extension of the method to the two dimensional case is discussed the one dimensional version is illustrated with some probabilistic examples involving both explicit and implicit functions the accuracy achieved in these examples with using the standard double precision arithmetic evaluated in terms of relative errors is about 10 10 10 14 even in case of out of scale parameters computational aspects are discussed in comparison with previously known realizations of the post widder method

magnetothermoelasticity with two relaxation times in conducting medium with variable electrical and thermal conductivity the equations of magneto thermoelasticity with two relaxation times and with variable electrical and thermal conductivity for one dimensional problems including heat sources are cast into matrix form using the state space and laplace transform techniques the resulting formulation is applied to a problem for the whole conducting space with a plane distribution of heat sources it also is applied to a semispace problem with a traction free surface and plane distribution of heat sources located inside the conducting medium the inversion of the laplace transforms is carried out using a numerical approach numerical results for the temperature displacement and stress distributions are given and illustrated graphically for both problems a comparison is made with the results obtained in the following cases a the electrical and thermal conductivities have constant values b the absence of magnetic field and c the coupled theory in magneto thermoelasticity

evaluation of inverse fourier transforms through romberg integration this study deals with evaluation of inverse integral transforms through numerical integration arguments are presented to explain that such a numerical evaluation is mathematically incorrect in recent years a sudden increase has been noticed in the number of research publications in which romberg integration is said to have used in evaluating the inverse fourier transforms in this regard even the references cited in these papers do not support such an evaluation but suggest contrary an immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique

improved difference approximations to the heat equation a method for obtaining difference equations from differential equations which has previously been applied to ordinary differential equations is here applied to the time dependent heat conduction equation as a representative example of parabolic partial differential equations explicit difference equations are derived which are stable for all values of t 2 and are also accurate implicit algorithms with improved accuracy are also derived problems in cartesian and cylindrical co ordinates are treated

interactions due to mechanical thermal sources in a micropolar thermoelastic medium possessing cubic symmetry abstract the present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface analytic expressions for displacement components microrotation force stress couple stress and temperature distribution are obtained in the physical domain for lord shulman l s and green lindsay g l theories of thermoelasticity by applying integral transforms a numerical inversion technique has been applied to obtain the solution in the physical domain the numerical results are presented graphically for a particular model

sign and stability of equilibria in quasi monotone positive nonlinear systems the paper deals with the problem of finding the extension of a well established connection between sign and stability of nontrivial equilibria in positive linear systems to the class of quasi monotone positive nonlinear systems the mathematical framework to provide the sufficient conditions guaranteeing such a relationship is the stability theory for nonlinear systems especially the comparison principles and the method of vector lyapunov functions as an illustration of our results we present an example of a double effect evaporator to study the sign stability property of its only equilibrium point

a laplace transorm potential theoretic method for acoustic propagation in subsonic flows this paper introduces a competitive computational approach for determining time dependent far field sound generated by subsonic flows around lifting airfoils the procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil it is assumed that the sound pressure on the boundary of this enclosed region referred to as the kirchhoff surface is specified possibly by another procedure such as solving the full euler equations away from the kirchhoff surface the euler equations are linearized about a uniform mean flow it is well known that linearized euler equations can be uncoupled into a scalar convective wave equation however due to the anisotropy present in the convective wave equation it is difficult to compute solutions in this context direct numerical simulation of the convective wave equation requires proper numerical descriptions of far field boundary conditions which is a non trivial task moreover if accurate far field conditions can be formulated the computational cost of direct simulation can be prohibitive even in a modest computational domain in this paper we present an alternate solution procedure first the problem is transformed via the laplace transform with appropriate initial conditions into a reduced wave equation the convective term in the reduced wave equation is removed using a dependent variable transformation then we use gothert s rule to obtain a helmholtz like equation with complex wave number which is subsequently solved using double layer potential theory finally upon application of numerical inverse laplace transform techniques far field acoustic pressure is obtained as a function of space and time

on some critical problems for the fractional laplacian operator abstract we study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional laplacian 2 u u q u n n u 0 in u 0 on where r n is a smooth bounded domain n 1 0 0 q n n 0 min n 2 for suitable conditions on depending on q we prove in the case q 1 there exist at least two solutions for every 0 and some 0 at least one if no solution if for q 1 we show existence of at least one solution for 0 1 and nonexistence for 1 when q 1 the existence is shown for every 0 also we prove that the solutions are bounded and regular

exponential solution of a problem of two dimensional motion of micropolar fluid in a half plane in this paper we generalize the results of the homogenous equation in fluid mechanics in the half plane for the type of micropolar fluid when the shear stresses spin micro rotation and one component of the velocity are given on the boundary we use laplace fourier transforms and then we convert laplace transform to find the solution in laplace domain then the numerical solution is applied to obtain the real solution in the physical domain graphically

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

hybrid laplace transform finite difference method for transient heat conduction problems the new method involving the combined use of the laplace transform and the finite difference method is applicable to the problem of time dependent heat flow systems the present method removes the time derivatives from the governing differential equation using the laplace transform and then solves the associated equation with the finite difference method the transformed temperature is inverted numerically by the method of honig and hirdes to obtain the result in the physical quantities the present results are compared in tables with exact solutions and those obtained from the combined use of the laplace transform and the finite element method it is found that the present method is reliable and efficient

an explicit conditionally stable finite difference equation for heat conduction problems this paper reports a new explicit and conditionally stable finite difference equation for heat conduction it predicts results with an accuracy comparable with or better than that obtainable by other methods stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes some existing difference equations are special cases of the new equation reported in this paper the new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known

mechanical and thermal sources in a micropolar generalized thermoelastic medium abstract the disturbance due to mechanical and thermal sources in a homogeneous isotropic micropolar generalized thermoelastic half space is investigated by the use of laplace fourier transform technique the analytical expressions of displacement components normal force stress tangential force stress and temperature field so obtained have been inverted by using a numerical technique numerical results are presented graphically for a magnesium crystal like material

transient wave analysis of a cantilever timoshenko beam subjected to impact loading by laplace transform and normal mode methods abstract this study applies two analytical approaches laplace transform and normal mode methods to investigate the dynamic transient response of a cantilever timoshenko beam subjected to impact forces explicit solutions for the normal mode method and the laplace transform method are presented the durbin method is used to perform the laplace inverse transformation and numerical results based on these two approaches are compared the comparison indicates that the normal mode method is more efficient than the laplace transform method in the transient response analysis of a cantilever timoshenko beam whereas the laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi span timoshenko beam furthermore a three dimensional finite element cantilever beam model is implemented the results are compared with the transient responses for displacement normal stress shear stress and the resonant frequencies of a timoshenko beam and bernoulli euler beam theories the transient displacement response for a cantilever beam can be appropriately evaluated using the timoshenko beam theory if the slender ratio is greater than 10 or using the bernoulli euler beam theory if the slender ratio is greater than 100 moreover the resonant frequency of a cantilever beam can be accurately determined by the timoshenko beam theory if the slender ratio is greater than 100 or by the bernoulli euler beam theory if the slender ratio is greater than 400

a numerical treatment to the solution of quasiparabolic partial differential equations this paper presents results obtained by the implementation of a hybrid laplace transform finite element method to the solution of quasiparabolic problem the present method removes the time derivatives from the quasiparabolic partial differential equation using the laplace transform and then solves the associated equation with the finite element method the numerical inverse of the laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order test examples are used to show that the numerical solution is comparable to the exact solution of the initial boundary value problem at the given grid points

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

positive realizations of linear systems abstract this paper deals with the realization problem of linear systems in which a sign pattern is imposed on the realization a b c t this problem arises in the context of positive linear systems i e systems in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative using a unitary framework for continuous time and discrete time systems we derive necessary and sufficient conditions for positive realizability by means of convex analysis moreover the complete solution in the case of a transfer function of mcmillan degree n 3 is obtained

constrained exact controllability of semilinear systems in the paper infinite dimensional dynamical control systems described by semilinear abstract differential equations are considered using a generalized open mapping theorem sufficient conditions for constrained exact local controllability are formulated and proved it is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero constrained exact local controllability of semilinear abstract second order dynamical systems are also formulated and proved as an illustrative example constrained exact local controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented

an extension problem for the cr fractional laplacian we show that the conformally invariant fractional powers of the sub laplacian on the heisenberg group are given in terms of the scattering operator for an extension problem to the siegel upper halfspace remarkably this extension problem is different from the one studied among others by caffarelli and silvestre we also prove an energy identity that yields a sharp trace sobolev embedding

magnetohydrodynamic unsteady free convection flow of a couple stress fluid with one relaxation time through a porous medium the method of the matric exponential which constitutes the basis of the state space approach of modern control theory is applied to the non dimensional equations of a magnetohydrodynamic unsteady free convection flow of a couple stress fluid through a porous medium with one relaxation time the resulting formulation together with laplace transform technique is applied to a thermal shock problem also a problem with distribution of heat sources is considered numerical results for the velocity induced magnetic field angular velocity and temperature distributions are given and illustrated graphically for each problem

numerical solutions for the hyperbolic heat conduction problems in a layered solid cylinder with radiation surface the numerical scheme based on the hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic heat conduction problems in an infinitely long layered solid cylinder with the nonlinear boundary conditions in order to perform the laplace transform method the nonlinear boundary conditions are linearized with taylor s series expansion results show that the present numerical scheme can overcome the mathematical difficulties induced by the nonlinear boundary conditions the geometry the composite interface and the singular point and has stability and reliability for such problems effects of the thermal properties of two dissimilar materials on heat transfer are also discussed

numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance a hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic diffusion problems with the pulsed boundary conditions in various coordinate systems the laplace transform method is used to remove the time dependent terms in the governing differential equations and the boundary conditions and then the transformed equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities the results show that the numerical results agree well with the analytic solution and do not exhibit numerical oscillations in the vicinity of the jump discontinuity the present method also can solve the problems with the singular point

elastodynamics of an axisymmetric problem in an anisotropic liquid saturated porous medium the laplace and hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid saturated porous medium for plain axisymmetric problem in the transformed form an application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case to get the solutions in the physical form a numerical inversion technique has been applied the results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model

new hybrid laplace transform finite element method for three dimensional transient heat conduction problem the paper presents results obtained by the implementation of a new hybrid laplace transform finite element method developed by the authors the present method removes the time derivatives from the governing differential equation using the laplace transform and then solves the associated equation with the finite element method previously reported hybrid laplace transform finite element methods1 have been confined to one nodal solution at a time when applied to many nodes it takes an excessive amount of computer time by using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems test examples are used to show that the basic accuracy is comparable to that obtainable by analytical finite difference and finite element methods

passage times of asymmetric anomalous walks with multiple paths we investigate the transient and the long time behaviour of asymmetric anomalous walks in heterogeneous media two types of disorder are worked out explicitly weak and strong disorder in addition the occurrence of disordered multiple paths is considered we calculate the first passage time distribution of the associated stochastic transport process we discuss the occurrence of the crossover from a power law to an exponential decay for the long time behaviour of the distribution of the first passage times of disordered biased walks

on a numerical technique regarding inversion of the laplace transform abstract we have discussed a method to convert the laplace transform into an integral equation of the first kind of convolution type which is an ill posed problem and used a regularization method to solve it we investigated the behavior of the optimal regularization parameter the optimal choice of parameter in the regularization of ill posed inverse problems depends on several features of a given problem we have compared our results with varah s 1979 1983 results and they are shown in respective diagrams for comparison purposes

an application of the ltdrm to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions in this paper we shall present an application of the laplace transform dual reciprocity method ltdrm to the solution of transient diffusion problems with nonlinear material properties and nonlinear boundary conditions two methods with and without utilizing the kirchhoff transformation will be discussed the nonlinear terms in both governing equation and boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the laplace transformation and then the problem is solved by the dual reciprocity method as a result a solution at any specific time can be obtained without step by step calculations in time domain and computations of domain integrals to show the efficiency and accuracy of the present method several problems are analyzed and their solutions are compared with those obtained either analytically or numerically

aspects of positivity in control theory this paper studies finite and infinite dimensional linear control systems of the form df dt af bu where a is the infinitesimal generator of a c 0 semigroup that preserves a cone c and where bu takes values in c since the reachable states are all in c the system is not controllable in the usual sense of concern is positive controllability which means that the entire cone c can be approximately reached it turns out that positive controllability is rather difficult to achieve but that for stable systems an important subclass of states can be reached different examples are provided

the extended durbin method and its application for piezoelectric wave propagation problems abstract based on the well known durbin method an efficient numerical method was developed for the inversion of the two sided laplace transform the accuracy of the method was verified using examples as an application of the method transient elastic waves propagating in a two layered piezoelectric medium subjected to anti plane concentrated loading and in plane electric displacement loading were investigated one sided and two sided laplace transforms were applied to determine the shear stresses and electric displacements in the double laplace transform domain subsequently the durbin method for one sided laplace transform inversion and the extended durbin method for two sided laplace transform inversion were used to implement the numerical inversions additionally the numerical results of the transient stresses and electric displacements were evaluated and discussed it showed that the arrival time of transient waves satisfies physical phenomena and the transient solution oscillates near the static solution and rapidly approximates the static solution

a half space problem in the theory of generalized thermoelastic diffusion abstract in this work we consider the problem of a thermoelastic half space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time the bounding surface of the half space is taken to be traction free and subjected to a time dependent thermal shock the chemical potential is also assumed to be a known function of time on the bounding plane laplace transform techniques are used the solution is obtained in the laplace transform domain by using a direct approach the solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the laplace transform based on fourier expansion techniques the temperature displacement stress and concentration as well as the chemical potential are obtained numerical computations are carried out and represented graphically

effect of body forces on a 2d generalized thermoelastic long cylinder in this work we consider a two dimensional problem for an infinitely long solid cylinder the lateral surface of the cylinder is taken to be traction free and is subjected to a known temperature distribution under the action of solenoidal body forces laplace transform techniques are used the solution in the transformed domain is obtained by using a direct approach in the form of an infinite series the inverse laplace transforms are obtained by using a numerical method based on fourier expansion techniques numerical results are computed for the temperature displacement and stress distributions and shown graphically

numerical inversion of the laplace transform from the real axis a numerical method for inversion of the laplace transform f p given for p 0 only is proposed recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given the results of the numerical tests are discussed

equations involving fractional laplacian operator compactness and application abstract in this paper we consider the following problem involving fractional laplacian operator 1 u u 2 2 e u u in u 0 on where is a smooth bounded domain in r n e 0 2 2 0 1 2 2 n n 2 and is either the spectral fractional laplacian or the restricted fractional laplacian we show for problem 1 with the spectral fractional laplacian that for any sequence of solutions u n of 1 corresponding to e n 0 2 2 satisfying u n h c in the sobolev space h defined in 1 2 u n converges strongly in h provided that n 6 and 0 the same argument can also be used to obtain the same result for the restricted fractional laplacian an application of this compactness result is that problem 1 possesses infinitely many solutions under the same assumptions

liouville type theorems for nonlinear elliptic equations on extended grushin manifolds abstract in this paper we study two liouville theorems for nonlinear boundary value problems on extended grushin manifolds these problems are closely related to nonlinear fractional grushin equations we will prove that these problems do not possess nontrivial positive solution under some assumptions on the nonlinear terms we use the moving plane method in an integral form to prove our results

positive solutions of nonlinear problems involving the square root of the laplacian abstract we consider nonlinear elliptic problems involving a nonlocal operator the square root of the laplacian in a bounded domain with zero dirichlet boundary conditions for positive solutions to problems with power nonlinearities we establish existence and regularity results as well as a priori estimates of gidas spruck type in addition among other results we prove a symmetry theorem of gidas ni nirenberg type

state space approach to generalized thermoelastic problem with thermomechanical shock in this work the state space formulation for one dimensional problem of generalized thermoelasticity with one relaxation time is introduced the resulting formulation together with the laplace transform technique is applied to a thermomechanical shock half space problem the solution in the transformed domain is obtained the inverse laplace transforms is evaluated numerically the results are obtained and represented graphically

a simple and efficient algorithm to compute tail probabilities from transforms we present an algorithm to approximately compute the tail probability that a random variable exceeds a specified number given only an expression for its transform we also show that the problem is p hard more difficult than np hard suggesting that no efficient procedure can solve it exactly our method consists essentially of summing a power series and thus is easy to perform and requires little memory furthermore its computational effort is nearly linear in the reciprocal of a prespecified worst case error bound

a problem of numerical inversion of implicitly defined laplace transforms abstract a procedure is proposed for numerical inversion of laplace transforms x s implicitly defined from the functional equation x s g a s cx s where a and g are known functions c is a known constant this equation is encountered in queueing inventory and insurance problems the procedure constructs coefficients of the laguerre series for the original in the laguerre series inversion method and a sequence of approximants in the post widder inversion method scalar and matrix cases are treated in the same fashion the numerical results are compared with those attainable with the fourier series method

dynamic simulation of a bimodal ultrasonic motor by new hybrid laplace transform finite element method abstract a new hybrid laplace transform finite element method is proposed to solve the dynamic problem of a bimodal ultrasonic motor which used a piezoelectric beam to drive the rotor two modes longitudinal and flexural of the piezoelectric beam are simultaneously excited by only one power amplifier a set of differential equations is derived by finite element formulation for this oscillating beam a proper similarity transform technique is used to decouple the laplace transformed equations governing the vibration of the beam without contact and to make the inverse laplace transformation easier the contact problem between the beam and the rotor is also formulated and numerically solved it is found that the simulation results obtained by using this hybrid method are almost identical with those by the runge kutta method but the former is able to avoid an excessive amount of computation time some important factors affecting the behavior of this motor are studied including structure design amplitude of input voltage phase displacement exciting frequency gap between beam tip and rotor and contact phenomena