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An Efficient Numerical Scheme for Biological Models in the Frame of Bernoulli Wavelets

Computer Modeling in Engineering & Sciences 2023年第12期137卷 2381-2408页

作者： Fei Li Haci Mehmet Baskonus S.Kumbinarasaiah G.Manohara Wei Gao Esin Ilhan Department of Scientific Research Yunnan Normal UniversityKunming650500China Department of Mathematics and Science Education Harran UniversitySanliurfa63050Türkiye Department of Mathematics Bangalore UniversityBengaluru560056India School of Information Science and Technology Yunnan Normal UniversityKunming650500China Faculty of Engineering and Architecture Kirsehir Ahi Evran UniversityKırsehir40500Türkiye

This article considers three types of biological systems:the dengue fever disease model,the COVID-19 virus model,and the transmission of Tuberculosis *** new technique of creating the integration matrix for the Bernoulli wavelets is ***,the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme(BWCM).All three models are in the form system of coupled ordinary differential equations without an exact *** systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation *** numerical wave distributions of these governing models are obtained by solving the algebraic equations via the Newton-Raphson *** results obtained from the developed strategy are compared to several schemes such as the Runge Kutta method,and ND solver in mathematical *** convergence analyses are discussed through *** newly implemented Bernoulli wavelet method improves the accuracy and converges when it is compared with the existing methods in the literature.

关键词： Biological systems system of coupled ODEs bernoulli wavelets functional matrix collocation technique

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A Compressed Sensing Approach for Partial Differential Equations with Random Input Data

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Communications in Computational Physics 2012年第9期12卷 919-954页

作者： L.Mathelin K.A.Gallivan LIMSI-CNRS BP 13391403 OrsayFrance Mathematics Dpt. 208 Love Building1017 Academic WayFlorida State UniversityTallahassee FL 32306-4510USA

In this paper,a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is *** with Monte-Carlo and stochastic collocation methods,only point-wise evaluations of the stochastic output response surface are required allowing the use of legacy deterministic codes and precluding the need for any dedicated stochastic code to solve the uncertain problem of *** new approach differs from these standard methods in that it is based on ideas directly linked to the recently developed compressed sensing *** technique allows the retrieval of the modes that contribute most significantly to the approximation of the solution using a minimal amount of *** generation of this information,via many solver calls,is almost always the bottle-neck of an uncertainty quantification *** the stochastic model output has a reasonably compressible representation in the retained approximation basis,the proposedmethod makes the best use of the available information and retrieves the *** quantification of the solution of both a 2-D and 8-D stochastic Shallow Water problem is used to demonstrate the significant performance improvement of the new method,requiring up to several orders of magnitude fewer solver calls than the usual sparse grid-based Polynomial Chaos(Smolyak scheme)to achieve comparable approximation accuracy.

关键词： Uncertainty quantification compressed sensing collocation technique stochastic spectral decomposition Smolyak sparse approximation stochastic collocation

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