A numerical method for two-dimensional Hammerstein integral equations

In this paper we investigate a collocation method for the approximate solution of Hammerstein integral equations in two dimensions. As in [8], col- location is applied to a reformulation of the equation in a new unknown, thus reducing the computational cost and simplifying the implementation. We start with a special type of piecewise linear interpolation over triangles for a refor- mulation of the equation. This leads to a numerical integration scheme that can then be extended to any bounded domain in R², which is used in collocation. We analyze and prove the convergence of the method and give error estimates. As the quadrature formula has a higher degree of precision than expected with linear interpolation, the resulting collocation method is superconvergent, thus requiring fewer iterations for a desired accuracy. We show the applicability of the proposed scheme on numerical examples and discuss future research ideas in this area. Mathematics Subject Classification (2010): 41A15, 45B05, 47G10, 65D07, 65R20

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, which are based on discrete stochastic arithmetic (DSA), are applied to validate the numerical results of the HATM. Additionally, the stopping condition in the numerical algorithm is based on two successive approximations and the main theorem of the CESTAC method can aid us analytically to apply the new terminations criterion instead of the usual absolute error that we use in the floating-point arithmetic (FPA). Finding the optimal approximations and the optimal iteration of the HATM to solve the nonlinear fractional order model of COVID-19 are the main novelties of this studyThe work of J.J.N. has been partially supported by the Xunta de Galicia under grant ED431C 2019/02, as well as by Instituto de Salud Carlos III and the Ministerio de Ciencia e Innovación of Spain, research grant COV20/00617. The work of S. Noeiaghdam has been supported by a grant from the Academic Council in the direction of the scientific school of Irkutsk National Research Technical University No. 14-NSH-RAN-2020S

Working memory capacity moderates the effect of hearing aid experience on phonological processing performance

PurposeIndividuals with acquired hearing impairment often experience declines in phonological processing abilities, a phenomenon thought to be mediated by working memory capacity (WMC). However, the role of hearing aid use in this context remains underexplored. Therefore, in the current study, we aimed (1) to tease apart the effect of hearing impairment and hearing aid use on phonological processing performance, and (2) to investigate the effect of hearing aid use on phonological processing in more detail, while considering the involvement of WMC.MethodUsing mixed effect models, we investigated rhyme judgment performance and its reliance on WMC among three groups of participants: a group of hearing aid users (n = 202), a group of hearing-impaired individuals without hearing aid (n = 54), and a group of normal hearing controls (n = 201). We also examined how years of hearing aid use was associated with rhyme judgment performance and its reliance on WMC in hearing aid users.ResultsWe found that hearing impairment was associated with increased dependence of rhyme judgment performance on WMC regardless of the use of hearing aids. Furthermore, hearing aid use was overall positively associated with rhyme judgment performance, with this relationship influenced by variations in WMC.ConclusionWMC influences the effectiveness of hearing aids for phonological processing. This role may result from working memory’s involvement in the processing of output signals from hearing aids, as well as in the strategies hearing aid users implement to deal with phonological processing tasks