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Communications in Theoretical Physics 2021年第2期73卷 11-22页

作者： Nermeen A Elkot Mahmoud A Zaky Eid H Doha Ibrahem G Ameen Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt Department of Applied Mathematics National Research CentreDokkiCairo 12622Egypt Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt

While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts *** this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation *** collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of ***,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical *** existence and uniqueness of the numerical solution are *** experiments are provided to support the theoretical convergence *** results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.

关键词： spectral collocation method convergence analysis multi-dimensional integral equations

On the solution of the Human Immunodeficiency Virus(HIV)infection model using spectral collocation method

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International Journal of Biomathematics 2021年第2期14卷 15-40页

作者： Sagithya Thirumalai Rajeswari Seshadri Suayip Yuzbası Department of Mathematics Pondicherry UniversityKalapetPuducherry 605014India Department of Mathematics Akdeniz University TH-07058 AntalyaTurkey

In this research work,we study the Human Immunodeficiency Virus(HIV)infection on helper T cells governed by a mathematical model consisting of a system of three first-order nonlinear differential *** objective of the analysis is to present an approximate mathematical solution to the model that gives the count of the numbers of uninfected and infected helper T cells and the number of free virus particles present at a given instant of *** system of nonlinear ODEs is converted into a system of nonlinear algebraic equations using spectral collocation method with three different basis functions such as Chebyshev,Legendre and Jacobi *** factors such as the production of helper T cells and infection of these cells play a vital role in infected and uninfected cell *** error analysis is done to compare our results with the existing *** is shown that the spectral collocation method is a very reliable,efficient and robust method of solution compared to many other solution procedures available in the *** these results are presented in the form of tables and figures.

关键词： HIV infection model spectral collocation method Chebyshev polynomials Legendre polynomials Jacobi polynomials error analysis

A Novel Multidomain spectral collocation method for Computational Electromagnetics with Application to Optical Waveguides

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A Novel Multidomain Spectral Collocation Method for Computat...

A Two-Parameter Continuation method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices

第四届海峡两岸计算流体力学学术研讨会

作者： Jaw-Yen Yang and Chia-Chien Huang Computational Electromagnetics and Plasma Lab., Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan

＜正＞ We proposed a novel solution method using multidomain spectral collocation method for computational electromagnetics with application to the modal analysis of optical waveguides. The method is formulated in terms of the transverse magnetic fields. The use of domain decomposition divides the computational domain into a few subdomains at the interfaces of different materials. The transverse magnetic fields in each subdomain can be expanded by a set of orthogonal basis functions and patched by applying the electromagnetic boundary conditions. Additionally, a new technique for the a priori determination of the scaling factor in Gauss-type basis functions is introduced to reduce the computational effort choosing the optimum value. The high accuracy of spectral collocation method is kept by the present method but the poor convergence is improved while usual spectral collocation method with single domain where regions of discontinuous refractive index profiles exists. Computations of several two and three-dimensional waveguide structures have been tested for the accuracy and efficiency of the present method. Detailed comparisons of the present results with exact solutions or previously published data based on other methods are included..

关键词： spectral collocation method computational electromagnetics domain decomposition optical waveguides orthogonal basis function scaling factor..

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Communications in Computational Physics 2013年第2期13卷 442-460页

作者： Y.-S.Wang B.-W.Jeng C.-S.Chien Department of Applied Mathematics National Chung Hsing UniversityTaichung 402Taiwan Department of Mathematics Education National Taichung University of EducationTaichung 403Taiwan Department of Computer Science and Information Engineering Ching Yun UniversityJungli 320Taiwan

We study efficient spectral-collocation and continuation methods(SCCM)for rotating two-component Bose-Einstein condensates(BECs)and rotating two-component BECs in optical lattices,where the second kind Chebyshev polynomials are used as the basis functions for the trial function space.A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations(GPEs),where the classical tangent vector is split into two constraint conditions for the bordered linear *** results on rotating two-component BECs and rotating two-component BECs in optical lattices are *** results on the former are consistent with the published numerical results.

关键词： spectral collocation method second kind Chebyshev polynomials periodic potential bifurcation

A Pseudo-spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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Computer Modeling in Engineering & Sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

Numerical investigation of the flow of a micropolar fuid through a porous channel with expanding or contracting walls

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Propulsion and Power Research 2014年第3期3卷 133-142页

作者： M.T.Darvishi F.Khani F.G.Awad A.A.Khidir P.Sibanda Deparment of Mathematics Razi UniversityKermanshah 67149Iran School of Mathematical Sciences University of KwaZulu-NatalPrivate Bag X01ScottsvillePietermaritzburg 3209South Africa

In this paper,we study the flow of a micropolar fluid in a porous channel with expanding or contracting ***,we use spectral collocation method on the governing equations to obtain an initial approximation for the solution of *** using the obtained initial approximation,we apply the homotopy analysis method to obtain a recursive fomula for the solution.

关键词： Homotopy analysis method spectral collocation method Series solution Micropolar fluid

The Effects of an Inclined Magnetic Field, Brownian Motion, and Thermophoresis on the Flow of Electrically Conducting and Chemically Reacting Casson Nanofluids Using Soret-Dufour Mechanisms

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Advances in Nanoparticles 2022年第2期11卷 55-71页

作者： Toyin Wasiu Akaje Bakai Ishola Olajuwon Department of Mathematics Federal University of Agriculture Abeokuta Nigeria

This research explored the effects of an angled magnetic field, Brownian motion, and thermophoresis on the flow of an electrically conducting and chemically reacting Casson nanofluid under the influence of the Soret-Dufour mechanism. A set of partial differential equations is generated by the flow mode. The governing partial differential equations are solved numerically using the spectral collocation method after being transformed to self-similar forms. The effect of various fluid parameters on the velocity profile, temperature profile, and nanoparticle concentration is addressed. A quantitative agreement is observed when previous findings are compared to the current results. The skin friction, local Nusselt number, and local Sherwood number are also examined, and the results are presented in the table. This study discovered that the inclined magnetic field has a significant impact on the flow of the electrically conducting fluid by delaying its mobility within the boundary layer. The plastic dynamic viscosity, which acts as a barrier to fluid flow, is shown to degenerate the fluid velocity when the Casson parameter is increased. As a consequence, the findings may be used to improve thermal science instruments and increase industrial output.

关键词： Soret-Dufour Mechanism Casson Nanofluid Inclined Magnetic Field Boundary Layer spectral collocation method