Table 4 - uploaded by Domingo Gamez
Content may be subject to copyright.
Source publication
This work presents an analysis of the error that is committed upon having obtained the approximate solution of the nonlinear Fredholm-Volterra-Hammerstein integral equation by means of a method for its numerical resolution. The main tools used in the study of the error are the properties of Schauder bases in a Banach space.
Context in source publication
Context 1
... we realize that the choice of a particular j, determining the dyadic partition of the interval 0, 1 from the first 2 j 1 nodes, and in such a way that the error is less than a fixed positive ε, that is, x − x m < ε, can be easily determined practically: it suffices to compute, once again by means of Mathematica 7, the error. To this end, since it is measured in terms of the supnorm, we consider the nodes 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1 and maximum of the absolute values of the differences between the values of the exact solution and the approximation obtained for the third iteration m 3. The numerical tests are given in Table 4 and correspond to the nonlinear mixed Fredhol-Volterra-Hammerstein equations considered in Examples 4.1 and 4.2, respectively. ...
Similar publications
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting decay behavior of the observation in time, we establish a novel H{\"o}lder type stability estimate for a large ter...
The Fourier pseudo-spectral method has been studied for a one-dimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of convergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of...
This research introduces a methodology of error analysis classification based on teaching-learning human translation. The errors have been committed by students of the fourth-year Translation and Interpreting Degree (Universidad Autónoma de Madrid, Spain). This analysis uses 69 official translation scripts and papers (English-Spanish) representing...
Tides and river slope are fundamental characteristics of estuaries, but they are usually undersampled due to deficiencies in the spatial coverage of water level measurements. This study aims to address this issue by investigating the use of airborne lidar measurements to study tidal statistics and river slope in the Columbia River estuary. Eight pl...
The Cornell Caltech Atacama Telescope (CCAT) is a 25 m diameter telescope that will operate at wavelengths as short as 200 microns. CCAT will have active surface control to correct for gravitational and thermal distortions in the reflector support structure. The accuracy and stability of the reflector panels are critical to meeting the 10 micron HW...
Citations
... Typical examples of iterative approximate methods are the Picard iteration method [51,101], Runge-Kutta method and block by block method [76], optimal perturbation iteration method [77], Dzyadyk's iterative approximation method [94] and Mann iteration procedure [102]. Fixed point methods based on Schauder bases [21,29,33,98], Schauder basis in an adequate Banach space [58], rationalized Haar wavelet [68], and fixed point methods in extended b-metric space [71] have been used successfully. Approximate methods using block-pulse functions [52,61,67], Bernstein polynomials [59], Haar wavelets [4], hyperbolic basis functions [84] and Hosoya polynomials [85] have also been presented. ...
In this paper, a direct operator method is presented for the exact closed-form solution of certain classes of linear and nonlinear integral Volterra–Fredholm equations of the second kind. The method is based on the existence of the inverse of the relevant linear Volterra operator. In the case of convolution kernels, the inverse is constructed using the Laplace transform method. For linear integral equations, results for the existence and uniqueness are given. The solution of nonlinear integral equations depends on the existence and type of solutions ofthe corresponding nonlinear algebraic system. A complete algorithm for symbolic computations in a computer algebra system is also provided. The method finds many applications in science and engineering.
The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.
