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ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF systemS OF nonlinear differential equations (Ⅰ)

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Applied Mathematics and Mechanics(English Edition) 2001年第3期22卷 282-293页

作者： JIANG Fu-ru(江福汝) Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P R China

A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u' = nu, epsilon nu' + f(x, u, u')nu' - g(x, u, u') nu = 0 (0 < epsilon much less than 1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.

关键词： system of nonlinear differential equations boundary value problems asymptotic solution

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Efficient Numerical Scheme for the Solution of HIV Infection CD4^(+)T-Cells Using Haar Wavelet Technique

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Computer Modeling in Engineering & Sciences 2022年第5期131卷 639-653页

作者： Rohul Amin Suayip Yuzbasi Shah Nazir Department of Mathematics University of PeshawarPeshawar25120Pakistan Department of Mathematics Faculty of ScienceAkdeniz UniversityAntalyaTr-07058Turkey Department of Computer Science University of SwabiSwabi23430Pakistan

In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells *** this technique,the derivative in the nonlinear model is approximated by utilizing Haar *** value of the unknown function is obtained by the process of *** estimation is also discussed,which aims to reduce the error of numerical *** numerical results show that the method is simply *** results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the *** results show that the Haar technique is easy,precise and effective.

关键词： system of nonlinear differential equations HIV infection of CD4^(+)T-cells Broyden method Haar wavelet residual error estimation

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Shifted Boubaker Lagrangian approach for solving biological systems

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International Journal of Biomathematics 2018年第3期11卷 155-175页

作者： Kourosh Parand Hossein Yousefi Mina Fotouhifar Mehdi Delkhosh Mehdi Hosseinzadeh Department of Computer Sciences Shahid Beheshti University G.C. Tehran Iran Department of Cognitive Modelling Institute for Cognitive and Brain Sciences Shahid Beheshti University G. C. Tehran Iran Department of Computer Sciences Shahid Beheshti University G. C. Tehran Iran Iran University of Medical Sciences Tehran Iran Computer Science University of Human Development Sulaimaniyah Iraq

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus （HIV） infection model of CD4^＋T cells and the susceptible-infected-removed （SIR） epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian （SBL） method. This method reduces the solution of such system to a system of linear or non- linear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge-Kutta （RK4） method and with the solutions obtained by some other methods in the literature.

关键词： Hantavirus infection model HIV infection model of CD4^+T cells SIR epi- demic model system of nonlinear differential equations Lagrangian method Boubaker polynomials.

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