accuracy of approximations of solutions to fredholm equations by kernel methods approximate solutions to inhomogeneous fredholm integral equations of the second kind by radial and kernel networks are investigated upper bounds are derived on errors in approximation of solutions of these equations by networks with increasing model complexity the bounds are obtained using results from nonlinear approximation theory the results are applied to networks with gaussian and kernel units and illustrated by numerical simulations

barycentric interpolation collocation methods for solving linear and nonlinear high dimensional fredholm integral equations abstract in this article two barycentric interpolation collocation methods are proposed for solving linear and nonlinear high dimensional f r e d h o l m integral equations of the second kind the approaches respectively utilize the modified weighted l a g r a n g e functions and the novel rational functions as the interpolation basis functions they are effective schemes for evaluating the multidimensional undetermined function through the numerical strategies and some composite quadrature formulas the linear and nonlinear f r e d h o l m integral equations are transformed into the corresponding linear and nonlinear algebraic equations further we prove that the discrete collocation methods are equivalent to the n y s t r o m quadrature methods then the convergence analysis is established by the collectively compact theory moreover the error estimation of the approximate solution and the exact solution are also provided numerical examples are presented to illustrate the capability and efficiency of the techniques by compared with the classic l a g r a n g e interpolation collocation method and other methodologies

the discrete galerkin method for integral equations a general theory is given for discretized versions of the galerkin method for solving fredholm integral equations of the second kind the discretized galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the galerkin method the theoretical framework that is given parallels that of the regular galerkin method including the error analysis of the superconvergence of the iterated galerkin and discrete galerkin solutions in some cases the iterated discrete galerkin solution is shown to coincide with the nystrom solution with the same numerical integration method the paper concludes with applications to finite element galerkin methods

a numerical study of some radial basis function based solution methods for elliptic pdes abstract during the last decade three main variations have been proposed for solving elliptic pdes by means of collocation with radial basis functions rbfs in this study we have implemented them for infinitely smooth rbfs and then compared them across the full range of values for the shape parameter of the rbfs this was made possible by a recently discovered numerical procedure that bypasses the ill conditioning which has previously limited the range that could be used for this parameter we find that the best values for it often fall outside the range that was previously available we have also looked at piecewise smooth versus infinitely smooth rbfs and found that for pde applications with smooth solutions the infinitely smooth rbfs are preferable mainly because they lead to higher accuracy in a comparison of rbf based methods against two standard techniques a second order finite difference method and a pseudospectral method the former gave a much superior accuracy

linear transformations that preserve immanants abstract we characterize the linear transformations on matrices that preserve the immanants i e d t x d x for all x where is an irreducible character of degree greater than one on s n we present a necessary and sufficient condition for t to be invertible if it preserves the generalized matrix function d c and prove that the preservers of immanants are always nonsingular

non planar curvature and branching of arteries and non planar type flow in this study magnetic resonance imaging techniques have been used to examine the geometry of arterial curvature and branching in casts and in vivo and to measure the distribution of axial velocity in the associated flow it is found contrary to a widely held view that the geometry is commonly non planar moreover relatively small values of the parameters which render the geometry non planar appear significantly to affect the velocity distribution the findings suggest that non planarity is an important factor influencing arterial flows including wall shear the implications are not restricted to vascular biology pathology and surgery but may extend to the design of general piping systems

on linear preservers of immanants let n 3 and be an irreducible nonlinear character of sn we describe the set p consisting of those permutations sn for which there exists a matrix c mn d such that for all sn ni 1 ci i as a consequence we get an improvement of a theorem due to duffner

on the shear thinning and viscoelastic effects of blood flow under various flow rates the aim of this paper is to describe and discuss the results of numerical comparative study performed in order to demonstrate and quantify some of the most relevant non newtonian characteristics of blood flow in medium sized blood vessels namely its shear thinning and viscoelastic behavior the models studied in this work are the classical newtonian and oldroyd b models as well as their generalized shear thinning modifications numerical tests are performed on three dimensional geometries namely an idealized axisymmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images the numerical solution of the system of governing equations is obtained by a finite volume method on a structured grid model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non newtonian effects

hybrid function method and convergence analysis for two dimensional nonlinear integral equations in the current paper an efficient numerical method based on two dimensional hybrid of block pulse functions and legendre polynomials is developed to approximate the solutions of two dimensional nonlinear fredholm volterra and volterrafredholm integral equations of the second kind the main idea of the presented method is based upon some of the important benefits of the hybrid functions such as high accuracy wide applicability and adjustability of the orders of block pulse functions and legendre polynomials to achieve highly accurate numerical solutions by using the numerical integration and collocation method two dimensional nonlinear integral equations are reduced to a system of nonlinear algebraic equations the focus of this paper is to obtain an error estimate and to show the convergence analysis for the numerical approach under the l2 norm numerical results are presented and compared with the results from other existing methods to illustrate the efficiency and accuracy of the proposed method

numerical solution of linear fredholm integral equations via two dimensional modification of hat functions abstract in this work we approximate the solution of the linear fredholm integral equations by means of a new two dimensional modification of hat functions 2d mhfs and a new operational matrix of integration by this idea the basic equations will be changed into the associated systems of algebraic equations also an error analysis is provided under several mild conditions the method is computationally attractive and some numerical examples are provided to illustrate its high accuracy

numerical investigation of the non newtonian blood flow in a bifurcation model with a non planar branch the pulsatile flow of non newtonian fluid in a bifurcation model with a non planar daughter branch is investigated numerically by using the carreau yasuda model to take into account the shear thinning behavior of the analog blood fluid the objective of this study is to deal with the influence of the non newtonian property of fluid and of out of plane curvature in the non planar daughter vessel on wall shear stress wss oscillatory shear index osi and flow phenomena during the pulse cycle the non newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior the non planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of wss along the vessel in particular in systole phase downstream of the bifurcation the velocity profiles are shifted toward the flow divider and low wss and high shear stress temporal oscillations characterized by osi occur on the outer wall region of the daughter vessels close to the bifurcation secondary motions become stronger with the addition of the out of plane curvature induced by the bending of the vessel and the secondary flow patterns swirl along the non planar daughter vessel a significant difference between the non newtonian and the newtonian pulsatile flow is revealed during the pulse cycle however reasonable agreement between the non newtonian and the rescaled newtonian flow is found calculated results for the pulsatile flow support the view that the non planarity of blood vessels and the non newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology

a new spectral meshless radial point interpolation smrpi method for the two dimensional fredholm integral equations on general domains with error analysis in this article we present a numerical method to solve two dimensional fredholm integral equations of the second kind on general domains the method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method the point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods these basis functions shape functions have kronecker delta function property since the proposed method is meshless it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional integral equation to the solution of a linear system of algebraic equations convergence analysis with error estimates are given with full discussion furthermore some numerical examples are presented to show the validity and efficiency of smrpi

a computational method for solving nonlinear stochastic volterra integral equations in this paper an efficient method for solving nonlinear stochastic ito volterra integral equations nsivies is proposed by using new adjustment of hat basis functions and their stochastic operational matrix of integration the nsivie is reduced to a nonlinear system of algebraic equations also the error analysis of the proposed method is investigated and proved that the order of convergence is o h 4 finally numerical examples affirm the efficiency of the proposed method

a study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions recent computational fluid dynamics cfd studies relate abnormal blood flow to rupture of cerebral aneurysms however it is still debated how to model blood flow with sufficient accuracy common assumptions made include newtonian behaviour of blood traction free outlet boundary conditions and inlet boundary conditions based on available literature these assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature however the consequences of these assumptions have so far been inadequately addressed this study investigates the effects of 4 different viscosity models 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms the differences are quantified in terms of 3 different wall shear stress wss metrics involving maximal wss average wss and proportion of aneurysm sac area with low wss the results were compared with common geometrical metrics such as volume aspect ratio size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type the results demonstrate strong correlations between the different viscosity models and boundary conditions the correlation between the different wss metrics range from weak to medium no strong correlations were found between the different wss metrics and the geometrical metrics or classifications

linear preservers of immanants on symmetric matrices abstract let q n c denote the space of the n square skew symmetric complex matrices and let be an irreducible nonlinear complex character of the symmetric group s n with n 1 1 2 1 n 2 we describe the linear operators of q n c that preserve the immanant d

numerical solution of the nonlinear fredholm integral equations by positive definite functions a numerical method for solving the nonlinear fredholom integral equations is presented the method is based on interpolation by radial basis functions rbf to approximate the solution of the fredholm nonlinear integral equations several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method

numerical solution of a class of mixed two dimensional nonlinear volterra fredholm integral equations using multiquadric radial basis functions an efficient numerical method is proposed for solving the mixed nonlinear volterra fredholm two dimensional integral equations ies using two dimensional radial basis functions rbfs this method is based on interpolation by radial basis functions including multiquadrics mqs using legendre gauss lobatto nodes and weights also a theorem is proved for convergence analysis some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method

dynamic curvature strongly affects wall shear rates in a coronary artery bifurcation model this study was motivated by the need for a better understanding of coronary artery blood flow patterns and their possible role in atherosclerosis formation of particular interest in this study was the effects of the dynamic deformation due to myocardial contraction on wall shear rate patterns in the coronary arteries a better understanding of these effects on wall shear rate in a bifurcation geometry and an evaluation of the importance of these effects was desired a three dimensional computer model of a bifurcation lying on the surface of a sphere with time varying radius of curvature was employed to simulate the motion and deformation of the arteries the results indicated low mean shear rates along the myocardial wall and very high shear rate variations over 100 of the static mean shear rate along the outer wall the results obtained using a quasi static analysis were found to underestimate the dynamic wall shear rate variation along the myocardial and outer walls it was concluded that dynamic geometry effects are important in determining sites of low mean and oscillating wall shear that have been associated with atherogenesis in curved bifurcating arteries

numerical solutions of nonlinear two dimensional partial volterra integro differential equations by haar wavelet a non linear kernel comprising a function of partial derivatives of arbitrary order is approximated by theorem 2 in ref 12 after substituting the kernel approximation in the original equation a nonlinear system is obtained using the haar wavelet solving the nonlinear system the nonlinear two dimensional integro differential volterra equation with partial derivatives is converted to a simple equation containing partial derivatives solving this simple equation we can approximate the solution of the nonlinear two dimensional integro differential volterra equation

a pseudospectral method for hammerstein equations abstract this paper considers hammerstein equations formula and presents a pseudospectral method for solving them numerically the method is applied to approximate the solution not to the equation in its original form but rather to an equivalent equation z t g t y t the function z is approximated by a polynomial z n of degree n with coefficients determined by collocation at the legendre gauss lobatto nodes we define the desire approximation to y by formula and establish that under suitable conditions lim n y n t y t uniformly in t advantages of the proposed method compared with existing methods in the literature are discussed an illustrative example is included to show the accuracy of the proposed method

applying the modified block pulse functions to solve the three dimensional volterra fredholm integral equations the main aim of this work is to give further studies for the multi dimensional integral equations in this work we solve special types of the three dimensional volterra fredholm linear integral equations of the second kind via the modified block pulse functions some theorems are included to show convergence and advantage of the method we solve some examples to investigate the applicability and simplicity of the method the numerical results confirm that the method is efficient and simple

numerical methods for fredholm integral equations on the square abstract in this paper we shall investigate the numerical solution of two dimensional fredholm integral equations by nystrom and collocation methods based on the zeros of jacobi orthogonal polynomials the convergence stability and well conditioning of the method are proved in suitable weighted spaces of functions some numerical examples illustrate the efficiency of the methods

the influence of the non newtonian properties of blood on the flow in large arteries unsteady flow in a 90 curved tube a numerical and experimental investigation of unsteady entry ow in a 903 curved tube is presented to study the impact of the non newtonian properties of blood on the velocity distribution the time dependent ow rate for the newtonian and the nonnewtonian blood analog uid were identical for the numerical computation a carreau yasuda model was employed to accommodate the shear thinning behavior of the xanthan gum solution the viscoelastic properties were not taken into account the experimental results indicate that signi cant di erences between the newtonian and non newtonian uid are present the numerical results for both the newtonian and the non newtonian uid agree well with the experimental results since viscoelasticity was not included in the numerical code shear thinning behavior of the blood analog uid seems to be the dominant non newtonian property even under unsteady ow conditions finally a comparison between the non newtonian uid model and a newtonian uid at a rescaled reynolds number is presented the rescaled reynolds number based on a characteristic rather than the high shear rate viscosity of the xanthan gum solution was about three times as low as the original reynolds number comparison reveals that the character of ow of the non newtonian uid is simulated quite well by using the appropriate reynolds number 1999 elsevier science ltd all rights reserved

richardson extrapolation of iterated discrete galerkin solution for two dimensional fredholm integral equations in this paper we study the numerical solution of two dimensional fredholm integral equation by discrete galerkin and iterated discrete galerkin method we are able to derive an asymptotic error expansion of the iterated discrete galerkin solution this expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth the expansion gives rise to richardson type extrapolation schemes which rapidly improve the original rate of the convergence numerical experiments confirm our theoretical results

an efficient approach to study the pulsatile blood flow in femoral and coronary arteries by differential quadrature method abstract in this paper flow analysis for a non newtonian third grade blood in coronary and femoral arteries is simulated numerically blood is considered as the third grade non newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient differential quadrature method dqm and crank nicholson method cnm are used to solve the partial differential equation pde governing equation by which a good agreement between them was observed in the results the influences of some physical parameters such as amplitude lead angle and body acceleration frequency on non dimensional velocity and profiles are considered for instance the results show that increasing the amplitude a g and reducing the lead angle of body acceleration make higher velocity profiles in the center line of both arteries

numerical solution based on two dimensional orthonormal bernstein polynomials for solving some classes of two dimensional nonlinear integral equations of fractional order abstract in this paper we develop a numerical scheme based on two dimensional orthonormal bernstein polynomials 2d obps to solve two dimensional nonlinear integral equations of fractional order the fractional integral considered here is in the riemann liouville sense by using definition of riemann liouville fractional integral two dimensional nonlinear fractional integral equations is transformed into two dimensional nonlinear ordinary integral equations operational matrices method based on 2d obps are applied to obtain an approximate solution with high accuracy for these equations in addition error analysis of the proposed method is discussed and an upper error bound is provided under weak assumptions some linear and nonlinear examples are given to demonstrate the accuracy efficiency and speed of the suggested method

pulsatile flow of non newtonian fluids through arterial stenoses the problem of blood flow through stenoses is solved using the incompressible generalized newtonian model the herschel bulkley bingham and power law fluids are incorporated the geometry corresponds to a rigid circular tube with a partial occlusion calculations are performed by a galerkin finite element method for the pulsatile case a predictor corrector time marching scheme is used with an adaptive time step results are obtained for steady and pulsatile physiological flows computations show that the memory effects taken into account in the model affect deeply the flow compared with newtonian reference case the disturbances are stronger by their vorticity intensity and persist after the geometrical obstacle this is especially true for severe stenoses

assessment of blood volume flow in slightly curved arteries from a single velocity profile abstract non invasive estimation of arterial blood volume flow bvf has become a central issue in assessment of cardiovascular risk poiseuille and womersley approaches are commonly used to assess the bvf from centerline velocity but both methods neglect the influence of curvature based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine the bvf can also be estimated by averaging velocities at opposite radial positions referred to as the cosine model ctm this study investigates the accuracy of bvf estimation in slightly curved arteries for bvf waveforms obtained in the brachial artery of 6 volunteers computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles the bvf was then estimated from the simulation results with the ctm and methods based on poiseuille womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed and compared to the prescribed bvf the simulations show that the influence of curvature is strongest when the flow decelerates for poiseuille and womersley the time average bvf was underestimated by maximally 10 4 and 7 8 for a radius of curvature of 50 and 100 mm respectively the estimation error is lower for the ctm and equals 4 2 and 1 2 for a radius of curvature of 50 and 100 mm respectively from this study we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the womersley method should be chosen the ctm improves current estimation techniques if in vivo velocity distributions are available

an efficient numerical approximation for the linear class of mixed integral equations in this paper an efficient numerical and analytical method for the linear class of mixed integral equations is presented the bivariate chebyshev collocation method for solving the linear volterra fredholm integral equations of the second kind is examined theoretically and numerically its focus lies mainly on the truncated bivariate chebyshev expansion and chebyshev collocation points

multiquadric interpolation improved abstract our concern in this paper is the improvement of localization properties of multiquadric interpolation on a multivariate integer grid

new algorithms for the numerical solution of nonlinear fredholm and volterra integral equations using haar wavelets two new algorithms based on haar wavelets are proposed the first algorithm is proposed for the numerical solution of nonlinear fredholm integral equations of the second kind and the second for the numerical solution of nonlinear volterra integral equations of the second kind these methods are designed to exploit the special characteristics of haar wavelets in both one and two dimensions formulae for calculating haar coefficients without solving the system of equations have been derived these formulae are then used in the proposed numerical methods in contrast to other numerical methods the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations the methods are validated on test problems and numerical results are compared with those from existing methods in the literature

numerical solution of the two dimensional fredholm integral equations using gaussian radial basis function in this paper we introduce a numerical method for the solution of two dimensional fredholm integral equations the method is based on interpolation by gaussian radial basis function based on legendre gauss lobatto nodes and weights numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method

two dimensional triangular functions and their applications to nonlinear 2d volterra fredholm integral equations two dimensional orthogonal triangular functions 2d tfs are presented as a new set of basis functions for expanding 2d functions their properties are determined and an operational matrix for integration obtained furthermore 2d tfs are used to approximate solutions of nonlinear two dimensional integral equations by a direct method since this approach does not need integration all calculations can be easily implemented and several advantages in reducing computational burdens arise finally the efficiency of this method will be shown by comparison with some numerical results

a meshless method for solving nonlinear two dimensional integral equations of the second kind on non rectangular domains using radial basis functions with error analysis in this paper we present a numerical method for solving two dimensional nonlinear fredholm integral equations of the second kind on a non rectangular domain the method utilizes radial basis functions rbfs constructed on scattered points as a basis in the discrete collocation method the proposed scheme is meshless since it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations error analysis is presented for this method finally numerical examples are included to show the validity and efficiency of the new technique