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 evaluation of highly oscillatory bessel transforms abstract in this paper we mainly focus on numerical evaluation of highly oscillatory bessel transforms based on the multiple integral the schemes for computing this class of the transform are presented by means of the bounds of special functions we give the corresponding errors of the schemes to demonstrate the efficiency and accuracy of the proposed methods some test examples are shown

numerical methods for two classes of singularly oscillatory bessel transforms and their error analysis abstract this work introduces and analyzes both the complex integration method and the modified complex integration method for two classes of highly oscillatory bessel transforms with algebraic or algebraic logarithmic singularities we first transform the original integrals into the infinite integrals on 1 by the change of variable t x where 0 with the help of the integral representation of the bessel function the integral representation and the asymptotic series of the whittaker function we then use the cauchy s residue theorem and convert the above infinite integrals into the infinite integrals on 0 the integrands of the resulting infinite integrals are not oscillatory and decay exponentially fast fortunately they can be efficiently evaluated by using the gauss laguerre quadrature rule furthermore we conduct their error analysis in inverse powers of the frequency finally numerical experiments are provided to confirm our theoretical analysis we can see from theoretical analysis and numerical experiments that the accuracy of the quadrature increases both for the case of growing the number of nodes n and fixed and for the case of an increasing and fixed the number of nodes n the comparison of the proposed two methods and the filon type method presented in kang and ma 2017 is briefly discussed as well

on the evaluation of infinite integrals involving bessel functions abstract in this paper we consider the numerical method for computing the infinite highly oscillatory bessel integrals of the form a f x c v x dx where c v x denotes bessel function j v x of the first kind y v x of the second kind h v 1 x and h v 2 x of the third kind f is a smooth function on a lim x f k x 0 k 0 1 2 is large and a 1 k with k 1 we construct the method based on approximating f by a combination of the shifted chebyshev polynomial so that the generalized moments can be evaluated efficiently by the truncated formula of whittaker w function the method is very efficient in obtaining very high precision approximations if is sufficiently large furthermore we give the error which depends on the endpoint a numerical examples are provided to confirm our results

on the implementation of discontinuous galerkin methods for volterra integral equations with highly oscillatory bessel kernels in this paper we consider implementation of discontinuous galerkin methods for weakly singular volterra integral equations of first and second kinds with highly oscillatory bessel kernels which cost the same operations independent of large values of frequencies preliminary numerical results show that the proposed method is efficient for verifying accuracy of approximate solutions

note on the homotopy perturbation method for multivariate vector value oscillatory integrals this paper considers a homotopy perturbation method for approximating multivariate vector value highly oscillatory integrals the asymptotic formulae of the integrals and the asymptotic order of the asymptotic method are presented numerical examples show the efficiency of the approximation method

a method for computing bessel function integrals abstract a method for numerical calculation of integrals containing bessel functions of integer or integer plus one half order is described the calculation involves first a one dimensional fourier sine or cosine transform followed by evaluation of the coefficient of the chebyshev series of the fourier transformed function in the case of the bessel function and evaluation of the legendre expansion coefficient in the case of the spherical bessel function a generalization of the method for the computation of an integral involving the bessel function of arbitrary real order v is presented as well

modelling merging and fragmentation in multiphase flows with surfer we introduce a new numerical method called surfer for the simulation of two and three dimensional flows with several fluid phases and free interfaces between them we consider incompressible fluids obeying the navier stokes equation with newtonian viscosity in the bulk of each phase capillary forces are taken into account even when interfaces merge or break up fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm thus allowing for full symmetry between fluid phases the navier stokes equation is solved using staggered finite differences on a mac grid and a split explicit time differencing scheme while incompressibility is enforced using an iterative multigrid poisson solver capillary effects are represented as a stress tensor computed from gradients of the volume fraction function this formulation is completely independent of the topology of interfaces and relatively easy to implement in 3d it also allows exact momentum conservation in the discretized algorithm numerical spurious effects or parasite currents are noticed and compared to similar effects in boltzmann lattice gas methods for immiscible fluids simulations of droplets pairs colliding in 2d and in 3d are shown interface reconnection is performed easily despite the large value of capillary forces during reconnection

procedures for computing one and two dimensional integrals of functions with rapid irregular oscillations a collocation procedure for efficient integration of rapidly oscillatory functions is presented the integration problem is transformed into a certain o d e problem and this is solved by a collocation technique the method is also extended to two dimensional integration and some numerical results are appended showing the efficiency of the method in handling difficult cases of rapid irregular oscillations 1 the procedure for one dimensional integrals we consider integrals of the form a 1 1 1 f x e iq x dx where f is smooth and nonoscillatory and iq x i b a 1 two practical methods for evaluating rapidly oscillatory integrals are described in 1 the use of approximation as in filon s method 3 4 and the speedup method of longman 5 formally both methods are applicable to any integral of the form 1 1 but their best performance is for the case of a constant frequency q w in this note we present an efficient method which is applicable for cases of varying frequency q using only a small number of values of f and q in a b and the values q a and q b the proposed method follows the spirit of filon s method it is based upon the fact that if f were of the form 1 2 f x iq x p x p x l l1p x a x b then the integral could be evaluated directly as 1 3 j b iq x p x pt x eiq x dx f d p x eiq x dx b e qbp a eiqa equation 1 2 can be considered as a differential equation for p x and any solution of this equation can be used in 1 3 for evaluating i the general solution of this equation is 1 4 p x e iq x f t eiq t dt cj received march 24 1981 revised july 29 1981 1980 mathematics subject classification primary 65d30 secondary 65d32 1982 american mathematical society 0025 5718 8 1 ooo 0 1 23 03 25 531 this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 36 01 utc all use subject to http about jstor org terms

optimality conditions and lagrangian duality in continuous time nonlinear programming abstract using a perturbation approach the kuhn tucker saddlepoint and stationary point optimality conditions and a lagrangian duality theory are established for a general class of continuous time nonlinear programming problems it is shown that most of the duality formulations in the existing literature of continuous programming are special cases of this lagrangian formulation

efficient calculation and asymptotic expansions of many different oscillatory infinite integrals abstract this paper introduces and analyzes quadrature rules and asymptotic expansions of a few highly oscillatory infinite integrals we first derive a series of useful asymptotic expansions in inverse powers of the frequency parameter which clarify the large behavior of these integrals then based on the resulting asymptotic expansions two different interpolatory quadrature rules are given one is the so called filon type methods based on standard hermite interpolation of the non oscillatory and non singular part of the integrands at equidistant nodes the other is the filon clenshaw curtis type method fcc by using special hermite interpolation at n 1 clenshaw curtis points and the fast computation of modified moments the interpolation coefficients needed in the fcc method can be computed by a numerically stable algorithm in o nlog n operations based on fast fourier transform fft the required modified moments can be accurately and efficiently calculated by some recurrence relation formulae moreover for these quadrature rules their error analyses in inverse powers of the frequency are provided the presented methods share the advantageous property that the accuracy improves greatly for fixed n as increases numerical examples show the accuracy and efficiency of the proposed methods

accurate representation of surface tension using the level contour reconstruction method some of the most demanding tests of interface methods for two phase flows with surface tension which use fixed eulerian grids occur at the two extremes of highly dynamic flows or static equilibrium conditions it has been difficult to design an interface method to operate accurately across this spectrum especially for 3d fluid flow calculations which on the one hand do not often have the required grid resolution to capture all of the fine scale structures that typically appear in highly stretched interfaces nor on the other hand the required accuracy in calculating surface tension forces we present improvements to the interface reconstruction procedure in the level contour reconstruction method lcrm j comput phys 180 2002 427 which now allow the reconstruction to proceed using a locally instead of a globally calculated contour value these improvements allow more precise control of the interface reconstruction in highly dynamic flows with coalescence and rupture and also avoid the problem of local mass redistribution in poorly resolved calculations in addition a new hybrid technique for surface tension calculation in the context of the front tracking method is demonstrated and shown to result in a marked improvement in suppressing parasitic currents by generally two orders of magnitude we compare and validate these new procedures in various test cases

fast integration of rapidly oscillatory functions a collocation method for approximating integrals of rapidly oscillatory functions is presented the method is efficient for integrals involving bessel functions jv rx with large oscillation parameter r as well as for many other one and multi dimensional integrals of functions with rapid irregular oscillations

on the evaluation of bessel transformations with the oscillators via asymptotic series of whittaker functions in this paper we are concerned with numerical evaluation of bessel transformations with the oscillators first we rewrite the integrals by whittaker functions then based on the asymptotic series of whittaker functions the integrals are transformed into the problems involving the complex exponential functions which can be efficiently computed by using the complex integration method at the same time we obtain the entirely different asymptotic expansions from the references in particular the asymptotic expansions can be denoted by the incomplete gamma function the error analysis shows that the decay of the error drastically improves as the frequency grows the effectiveness and accuracy of the methods are tested for large arguments of bessel functions

asymptotic expansions of bessel anger and weber transformations in this paper we explore higher order numerical quadrature for the integrations of systems containing bessel anger and weber functions the method is constructed by finding the approximate solution of the differential equation and truncating the asymptotic series numerical examples based on theoretical results are presented to demonstrate the efficiency of the method

efficient method for the computation of oscillatory bessel transform and bessel hilbert transform abstract in this paper we study the numerical methods for the evaluation of two kinds of highly oscillatory bessel transforms firstly we rewrite both integrals as the sum of two integrals by rewriting the bessel function as a linear combination of whittaker w function we then transform one of integrals into the fourier type which can be transformed into the integrals on 0 and can be computed by some proper gaussian quadrature which take into account the asymptotic property of whittaker w function as x 0 the other can be efficiently computed based on the evaluation of special functions in addition error analysis for the presented methods is given moreover we also give an explicit formula for the integral 0 j x x d x in terms of meijer g function and then apply the method for the oscillatory bessel transforms to the computation of highly oscillatory bessel hilbert transforms theoretical results and numerical examples demonstrate the efficiency and accuracy of the proposed methods

a continuous time generalization of gordan s transposition theorem abstract a certain infinite dimensional generalization of gordan s transposition theorem is obtained as a consequence of a strong duality principle in continuous time programming some implications and corollaries of the main theorem are also discussed

numerical integration of oscillatory airy integrals with singularities on an infinite interval abstract this work is devoted to the quadrature rules and asymptotic expansions for two classes of highly oscillatory airy integrals on an infinite interval we first derive two important asymptotic expansions in inverse powers of the frequency then based on structure characteristics of the two asymptotic expansions in inverse powers of the frequency both the so called filon type method and the more efficient clenshaw curtis filon type method are introduced and analyzed the required moments in the former can be explicitly expressed by the meijer g functions the latter can be implemented in o n log n operations based on fast fourier transform fft and fast computation of the modified moments here we can construct two useful recurrence relations for computing the required modified moments accurately with the help of the airy s equation and some properties of the chebyshev polynomials particularly we also provide their error analyses in inverse powers of the frequency furthermore the presented error analysis shows the advantageous property that the accuracy improves greatly as increases numerical examples are provided to illustrate the efficiency and accuracy of the proposed methods

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

method for numerical integration of rapidly oscillating functions in diffraction theory the quadrature of general highly oscillatory integrals is a relatively complicated computational problem that occurs in a wide range of practical applications e g in physics chemistry and image analysis it is often necessary to use a high number of nodal points with classical quadrature formulas in order to achieve a required accuracy of numerical integration of rapidly oscillating functions however an increase in integration points leads to a larger computational time our work describes and analyses a method for numerical integration of rapidly oscillating functions which enables to obtain the required accuracy with a smaller number of nodal points than classical integration rules and with a relatively simple integration formula the proposed method is generally suitable for integration of rapidly oscillating functions in various applications the method is demonstrated in examples of calculation of the diffraction integral in optics where the integrand is often a rapidly oscillatory function the results can be readily adapted to similar problems from other fields copyright 2009 john wiley sons ltd

laplace transforms for approximation of highly oscillatory volterra integral equations of the first kind abstract this paper focuses on laplace and inverse laplace transforms for approximation of volterra integral equations of the first kind with highly oscillatory bessel kernels where the explicit formulae for the solution of the first kind integral equations are derived from which the integral equations can also be efficiently calculated by the clenshaw curtis filon type methods furthermore by applying the asymptotics of the solution some simpler formulas for approximating the solution for large values of the parameters are deduced preliminary numerical results are presented based on the approximate formulae and the explicit formulae which are compared with the convolution quadrature and numerical inverse laplace transform methods all these methods share that the costs the same independent of large values of frequencies

a numerical method for the simulation of low mach number liquid gas flows this work is devoted to the numerical simulation of liquid gas flows the liquid phase is considered as incompressible while the gas phase is treated as compressible in the low mach number approximation a single fluid two pressure model is developed and the front tracking method is used to track the interface navier stokes equations coupled with that of temperature are solved in the whole computational domain velocity pressure and temperature fields are computed yielding a complete description of the dynamics for both phases we show that our method is much more efficient than the so called all mach methods involving a single pressure since large time steps can be used while retaining time accuracy the model is first validated on a reference test problem solved using an accurate ale technique to track the interface numerical examples in two space dimensions are next presented they consist of air bubbles immersed in a closed cavity filled up with liquid water the forced oscillations of the system consisting of the air bubbles and the liquid water are investigated they are driven by a heat supply or a thermodynamic pressure difference between the bubbles

algorithm for the computation of bessel function integrals abstract a fortran subroutine is given for the computation of integrals of the form c 0 f x j v x d x where v 0 1 10

on van der corput type lemmas for bessel and airy transforms and applications abstract this paper presents van der corput type lemmas for bessel and airy transforms with shifted jacobi weight functions these results on the asymptotic orders of the highly oscillatory integrals on the frequency are optimal furthermore from these estimates the convergence rates on filon type methods are easily derived

computation of oscillatory integrals with an exponential kernel and jacobi type singularities abstract in this communication two rules are considered for computing oscillatory integrals with an exponential kernel and jacobi type singularities an asymptotic rule is presented with the aid of integration by parts an asymptotic filon type quadrature rule is constructed on the basis of a two point taylor interpolation polynomial error analysis on the proposed rules in inverse powers of large frequency is provided numerical examples are provided to illustrate that the two rules are very efficient in obtaining very high precision approximations if is sufficiently large

letter to the editor on the filon and levin methods for highly oscillatory integral this paper shows that for any suitably smooth function f x and arbitrarily selected interpolation nodes c1 c2 cv in a b the filon method and the levin method for with the polynomial interpolation approach are identical when g x is a linear function based on this result a new efficient levin quadrature for is presented

unified formulation for compressible and incompressible flows by using multi integrated moments ii multi dimensional version for compressible and incompressible flows following our previous paper on a novel finite volume formulation for computing flows of any mach number we present the multi dimensional extension of the method in this paper treating two kinds of averages which are generically called moments and defined as the volume integrated average via and the surface integrated average sia in this paper as the prognostic variables makes the present method different from the conventional finite volume method where only via is the basic variable the resulting discretization approach which is a type of the cip multi moment finite volume method and called vsiam3 volume surface integrated average based multi moment method is combined with a pressure based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows the numerical algorithm for multi dimensions will be reported in this paper numerical experiments with flows of a wide range mach numbers will be also presented

on generalized quadrature rules for fast oscillatory integrals abstract in this paper we present numerical analysis for the generalized quadrature rule for a b f x w r x d x where w r x is an oscillatory function and derive higher order generalized quadrature rules the results show that the generalized quadrature rules are efficient for bessel trigonometric transformations and the accuracy increases when oscillation becomes faster

fast integration of highly oscillatory integrals with exotic oscillators in this paper we present an efficient filon type method for the integration of systems containing bessel functions with exotic oscillators based on a diffeomorphism transformation and give applications to airy transforms preliminary numerical results show the effectiveness and accuracy of the quadrature for large arguments of integral systems

nonsmooth continuous time optimization problems necessary conditions abstract we consider lipschitz continuous time nonlinear optimization problems and provide first order necessary optimality conditions of both fritz john and karush kuhn tucker types

a fast algorithm for the electromagnetic scattering from a large cavity a fast algorithm is presented for solving electromagnetic scattering from a rectangular open cavity embedded in an infinite ground plane the medium inside the cavity is assumed to be vertically layered by introducing a transparent artificial boundary condition the problem in the open cavity is reduced to a bounded domain problem a simple finite difference method is then applied to solve the model helmholtz equation the fast algorithm is designed for solving the resulting discrete system in terms of the discrete fourier transform in the horizontal direction a gaussian elimination in the vertical direction and a preconditioning conjugate gradient method with a complex diagonal preconditioner for the indefinite interface system the existence and uniqueness of the finite difference solution are established for arbitrary wave numbers our numerical experiments for large numbers of mesh points up to 16 million unknowns and for large wave numbers e g between 100 and 200 wavelengths show that the algorithm is extremely efficient the cost for calculating the radar cross section which is of significant interest in practice is o m2 for an m times m mesh the proposed algorithm may be extended easily to solve discrete systems from other discretization methods of the model problem

stability and convergence of collocation schemes for retarded potential integral equations time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations solving such equations numerically is both complicated and computationally intensive and numerical methods often prove to be unstable collocation schemes are easier to implement than full finite element formulations but little appears to be known about their stability and convergence here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering and use spatial fourier and temporal laplace transform techniques to demonstrate that such stable schemes are second order convergent

analysis of a collocation method for integrating rapidly oscillatory functions a collocation method for approximating integrals of rapidly oscillatory functions is analyzed the method is efficient for integrals involving bessel functions j rx with a large oscillation frequency parameter r as well as for many other one and multi dimensional integrals of functions with rapid irregular oscillations the analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases ko words oscillatory integrals collocation analysis

vector continuous time programming without differentiability in this work continuous time programming problems of vector optimization are considered firstly a nonconvex generalized gordan s transposition theorem is obtained then the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established a scalar dual problem is introduced and duality theorems are given no differentiability assumption is imposed

efficient evaluation of oscillatory bessel hilbert transforms in this paper we study the asymptotics and evaluation of the oscillatory bessel hilbert transform 0 f x email protected n wx dx with 0 t the singularity of the hilbert transform is transferred to an individual oscillatory integral independent of f x for this singular integral we present two methods one is the combination of a filon type method and a complex integration method the other is the combination of a filon type method and an adaptive clenshaw curtis quadrature the remaining integral which is nonsingular can be well calculated with a combination of a filon type method and a gauss laguerre quadrature the efficiency and accuracy of the proposed methods are illustrated by numerical examples

a sparse discretization for integral equation formulations of high frequency scattering problems we consider two dimensional scattering problems formulated as an integral equation defined on the boundary of the scattering obstacle the oscillatory nature of high frequency scattering problems necessitates a large number of unknowns in classical boundary element methods in addition the corresponding discretization matrix of the integral equation is dense we formulate a boundary element method with basis functions that incorporate the asymptotic behavior of the solution at high frequencies the method exhibits the effectiveness of asymptotic methods at high frequencies with only few unknowns but retains accuracy for lower frequencies new in our approach is that we combine this hybrid method with very effective quadrature rules for oscillatory integrals as a result we obtain a sparse discretization matrix for the oscillatory problem moreover numerical experiments indicate that the accuracy of the solution actually increases with increasing frequency the sparse discretization applies to problems where the phase of the solution can be predicted a priori for example in the case of smooth and convex scatterers

nonsmooth continuous time optimization problems sufficient conditions we discuss sufficient conditions of optimality for nonsmooth continuous time nonlinear optimization problems under generalized convexity assumptions these include both first order and second order criteria

a numerical method for two phase flow consisting of separate compressible and incompressible regions abstract we propose a numerical method for modeling two phase flow consisting of separate compressible and incompressible regions this is of interest for example when the combustion of fuel droplets or the shock induced mixing of liquids is numerically modeled we use the level set method to track the interface between the compressible and incompressible regions as well as the ghost fluid method gfm to create accurate discretizations across the interface the gfm is particularly effective here since the equations differ in both number and type across the interface the numerical method is presented in two spatial dimensions with numerical examples in both one and two spatial dimensions while three dimensional extensions are straightforward

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

a chebyshev collocation algorithm for 2d non boussinesq convection abstract a chebyshev collocation algorithm is developed to integrate the time dependent navier stokes equations for natural convection flow with large temperature differences the working fluid is assumed to be a perfect gas and its thermophysical properties vary with temperature according to sutherland laws the governing equations do not allow for acoustic waves the generalized helmholtz and uzawa operators which arise from time discretization are solved iteratively and the performances of several types of preconditioners and iterative schemes are examined the algorithm is validated by computing almost boussinesq flows and by comparing with previous results obtained with a finite difference algorithm we investigate the effects of the temperature difference and of total mass contained within the cavity on the transition to unsteadiness in a cavity of aspect ratio 8 it is shown that these parameters have indeed a significant effect on the value of rayleigh number at which unsteadiness is triggered we also discuss the nature of the time periodic solution which is obtained for ra slightly supercritical values

numerical approximations for highly oscillatory bessel transforms and applications abstract this paper presents an efficient numerical method for approximating highly oscillatory bessel transforms based on analytic continuation we transform the integrals into the problems of integrating the forms on 0 with the integrand that does not oscillate and decays exponentially fast which can be efficiently computed by using gauss laguerre quadrature rule we then derive the error of the method depending on the frequency and the node number moreover we apply the scheme for studying the approximations of the solutions of two kinds of highly oscillatory integral equations preliminary numerical results show the efficiency and accuracy of numerical approximations

efficient computation of highly oscillatory integrals with hankel kernel in this paper we consider the evaluation of two kinds of oscillatory integrals with a hankel function as kernel we first rewrite these integrals as the integrals of fourier type by analytic continuation these fourier type integrals can be transformed into the integrals on 0 the integrands of which are not oscillatory and decay exponentially fast consequently the transformed integrals can be efficiently computed by using the generalized gauss laguerre quadrature rule moreover the error analysis for the presented methods is given the efficiency and accuracy of the methods have been demonstrated by both numerical experiments and theoretical results

preinvex functions and weak efficient solutions for some vectorial optimization problem in banach spaces in this work we introduce the notion of preinvex function for functions between banach spaces by using these functions we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities moreover we will show that this class of problems has the property that each local optimal solution is in fact global

a chebyshev collocation method for a class of fredholm integral equations with highly oscillatory kernels based on the filon clenshaw curtis method for highly oscillatory integrals and together with the sommariva s result sommariva 2013 for clenshaw curtis quadrature rule we present a chebyshev collocation method for a class of fredholm integral equations with highly oscillatory kernels whose unknown function is assumed to be less oscillatory than the kernel in the proposed method the filon clenshaw curtis method is used to compute the involved oscillatory integrals which makes the proposed method very precise by solving only a small system of linear equations we can obtain a very satisfactory numerical solution the performance of the presented method is illustrated by several numerical examples compared with the method proposed by li et al 2012 this method enjoys a lower computational complexity furthermore numerical examples show that the presented method has a competitive advantage on the accuracy compared with the method in li et al 2012

optimality conditions in a vector continuous time optimization problem we consider nonlinear vector continuous time optimization problems with inequality type of constraints we derive new fritz john and karush kuhn tucker optimality conditions that are valid when all functions are preinvex

on the evaluation of highly oscillatory integrals by analytic continuation we consider the integration of one dimensional highly oscillatory functions based on analytic continuation rapidly converging quadrature rules are derived for a general class of oscillatory integrals with an analytic integrand the accuracy of the quadrature increases both for the case of a fixed number of points and increasing frequency and for the case of an increasing number of points and fixed frequency these results are then used to obtain quadrature rules for more general oscillatory integrals i e for functions that exhibit some smoothness but that are not analytic the approach described in this paper is related to the steepest descent method but it does not employ asymptotic expansions it can be used for small or moderate frequencies as well as for very high frequencies the approach is compared with the oscillatory integration techniques recently developed by iserles and norsett

sufficient optimality conditions in continuous time nonlinear programming abstract various first order sufficient optimality criteria for continuous time nonlinear programming problems with nonlinear equality and inequality constraints are established under generalized convexity assumptions and applications of these criteria to optimal control and continuous time fractional programming problems are briefly discussed

numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures numerical methods for strongly oscillatory and singular functions are given in this paper beside a summary of standard methods and product integration rules we consider a class of complex integration methods several applications of quadrature processes in problems in telecom munications and physics are also presented 1998 elsevier science ltd all rights reserved integration oscillatory kernel singular kernel orthogonal polynomials product rules gaussian quaclratures error function bessel functions legendre functions

on numerical computation of integrals with integrands of the form f x sin w xr on 0 1 with existing numerical integration methods and algorithms it is difficult in general to obtain accurate approximations to integrals of the form 0 1f x sin wx r dxor 0 1f x cos wx r dx r 0 where f is a sufficiently smooth function on 0 1 gautschi has developed software as scripts in matlab for computing these integrals for the special case r w 1 in this paper an algorithm as a mathematica program is developed for computing these integrals to arbitrary precision for any given values of the parameters in a certain range numerical examples are given of testing the performance of the algorithm program

the superconvergence of newton cotes rules for the hadamard finite part integral on an interval we study the general composite newton cotes rules for the computation of hadamard finite part integral with the second order singularity and focus on their pointwise superconvergence phenomenon i e when the singular point coincides with some a priori known point the convergence rate is higher than what is globally possible we show that the superconvergence rate of the composite newton cotes rules occurs at the zeros of a special function and prove the existence of the superconvergence points several numerical examples are provided to validate the theoretical analysis

on graded meshes for weakly singular volterra integral equations with oscillatory trigonometric kernels we compare the collocation methods on graded meshes with that on uniform meshes for the solution of the weakly singular volterra integral equation of the second kind with oscillatory trigonometric kernels due to in general unbounded derivatives at the left endpoint of the interval of integration we should approximate the solution of the integral equation by collocation methods on graded meshes however we show that this non smooth behavior of the solution has little effect on the approximate solution when the kernels of integral equation are highly oscillatory numerical examples are given to confirm the proposed results

efficient quadrature of highly oscillatory integrals using derivatives in this paper we explore quadrature methods for highly oscillatory integrals generalizing the method of stationary phase we expand such integrals into asymptotic series in inverse powers of the frequency the outcome is two families of methods one based on a truncation of the asymptotic series and the other extending an approach implicit in the work of filon filon 1928 proc r soc edinb 49 38 47 1 both kinds of methods approximate the integral as a linear combination of function values and derivatives with coefficients that may depend on frequency we determine asymptotic properties of these methods proving perhaps counterintuitively that their performance drastically improves as frequency grows the paper is accompanied by numerical results that demonstrate the potential of this set of ideas 1 ref 4

numerical simulation of free surface incompressible liquid flows surrounded by compressible gas a numerical model for the three dimensional simulation of liquid gas flows with free surfaces is presented the incompressible navier stokes equations are assumed to hold in the liquid domain in the gas domain the velocity is disregarded the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law the gas pressure is imposed as a normal force on the liquid gas interface an implicit splitting scheme is used to decouple the physical phenomena given the gas pressure on the interface the method described in j comput phys 155 1999 439 int j numer meth fluids 42 7 2003 697 is used to track the liquid domain and to compute the velocity and pressure fields in the liquid then the connected components of the gas domain are found using an original numbering algorithm finally the gas pressure is updated from the ideal gas law in each connected component of gas the implementation is validated in the frame of mould filling numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected

riemann problem and level set approaches for homentropic two fluid flow computations a finite volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities a novel ingredient in the method is a linearized two fluid osher scheme allowing for flux computations in the case of different fluids e g water and air left and right of a cell face a level set technique is employed to distinguish between the two fluids the level set equation is incorporated into the system of hyperbolic conservation laws fixes are presented for the solution errors pressure oscillations that may occur near two fluid interfaces when applying a capturing method the fixes are analyzed and tested for two fluid flows with arbitrarily large density ratios a simple variant of the ghost fluid method appears to be a perfect remedy computations for compressible water air flows yield perfectly sharp pressure oscillation free interfaces the masses of the separate fluids appear to be conserved up to first order accuracy

duality in nondifferentiable vector programming in this paper we study the saddle point optimality conditions and lagrange duality in multiobjective optimization for generalized subconvex like functions we obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined we also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem

continuous time optimization problems involving invex functions in d h martin the essence of invexity j optim theory appl 47 1985 65 76 martin introduced the notions of kkt invexity and wd invexity for mathematical programming problems these notions are relaxations of invexity in this work we generalize these concepts for continuous time nonlinear optimization problems we prove that the notion of kkt invexity is a necessary and sufficient condition for global optimality of a karush kuhn tucker point and that the notion of wd invexity is a necessary and sufficient condition for weak duality

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

fast computation of seabed spherical wave reflection coefficients in geoacoustic inversion this paper develops a fast numerical approach to computing spherical wave reflection coefficients swrcs for layered seabeds which provides substantial savings in computation time when used as the forward model for geoacoustic inversion of broadband seabed reflectivity data the approach exploits the sommerfeld integral representation of swrcs as the hankel transform of a function proportional to the plane wave reflection coefficient pwrc and applies levin integration to the rapidly oscillating integrand cast as the product of a pre computed media independent matrix and a vector involving pwrcs at a sparse sampling of integration angles compared to conventional simpson s rule integration for computation of the swrc the levin integration yields speed up factors of an order of magnitude or more further it results in reduced memory requirements for storage of pre computed quantities a desirable property when a graphics processing unit gpu is used for parallel computation of swrcs the paper applies trans dimensional bayesian inversion to investigate the impact of forward modeling in terms of pwrcs and swrcs on the estimation of geoacoustic parameters and uncertainties model comparisons are quantified in simulated and measured data inversions by comparing the estimated geoacoustic parameters to the true parameters or core measurements respectively and by calculating the deviance information criterion for model selection