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Ma’s Variation of Parameters Method for Fisher’s Equations

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Advances in Applied Mathematics and Mechanics 2010年第3期2卷 379-388页

作者： Syed Tauseef Mohyud-Din Ahmet Yıldırım HITEC University Taxila Cantt Pakistan Ege University Department of Mathematics35100 Bornova-IzmirTurkey

In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s *** suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or... 详细信息

关键词： Variation of parameters method variational iteration method nonlinear problems Fisher’s equation nonlinear diffusion equation error estimates

A study of nonlinear age-structured population models

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International Journal of Biomathematics 2016年第6期9卷 211-223页

作者： Syed Tauseef Mohyud-Din A. Waheed M. M. Ra.shidi Department of Mathematics Faculty of Sciences HITEC University Taxila Cantt Pakistan Department of Mathematics COMSATS Institute of Information Technology Attock Pakistan Shanghai Key Lab of Vehicle Aerodynamicsand Vehicle Thermal Management Systems Tongji University 3800 Cao An Road Jiading Shanghai 201803 P. R. China

This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method （MVIM） coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He＇s polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.

关键词： Age-structured population models nonlinear problems modified variationaliteration method auxiliary parameter correction functional.

Parareal-Richardson Algorithm for Solving nonlinear ODEs and PDEs

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Communications in Computational Physics 2009年第9期6卷 883-902页

作者： Shulin Wu Baochang Shi Chengming Huang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China

The parareal algorithm,proposed firstly by Lions et al.[***,***,and ***,A”parareal”in time discretization of PDE’s,*** Ser.I Math.,332(2001),pp.661-668],is an effective algorithm to solve the timedependent problems parallel in *** algorithm has received much interest from many researchers in the past *** present in this paper a new variant of the parareal algorithm,which is derived by combining the original parareal algorithm and the Richardson extrapolation,for the numerical solution of the nonlinear ODEs and *** nonlinear problems are tested to show the advantage of the new *** accuracy of the obtained numerical solution is compared with that of its original version(i.e.,the parareal algorithm based on the same numerical method).

关键词： Parallel computation parareal algorithm Richardson extrapolation accuracy nonlinear problems

A mathematical model to simulate Heap(bio)-leaching process:An exact conceptual model,Homotopy theory and comparative insights with conventional methods

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International Journal of Modeling, Simulation, and Scientific Computing 2017年第1期8卷 271-296页

作者： M.Yaghobi Moghaddam S.Z.Shafaei Tonkaboni M.Noaparast F.Doulati Ardejani School of Mining College of Engineering University of TehranP.O.Box 14395-515TehranIran

This paper attempts to address some nonlinear differential equations which describe main mechanisms governing heap(bio)leaching process as an important metallurgical facility in mining and mineral processing *** Homotopy Perturbation Method(HPM),Finite Volume Method and Analytical(Laplace)Method have been employed to provide proper solutions for these *** was made between the methods and agreement was close;considering the fact that the proposed solution in comparison with the others provided a remarkable accuracy in dealing with nonlinear problems associated with mining and mineral processing *** maximum error of HPM in relation to the analytical solution was *** numerical finite volume method incorporating a computational fluid dynamics model termed PHOENICS provided rational and accurate results;describing that many chemical and biological processes extremely affect the transportation mechanism of the aqueous compounds in a heap structure and subsequently on the process ***,all solution methods presented to simulate heap leaching process provided valuable information related to the time dependence concentrations of dissolved *** results obtained from this study can be effectively applied to manage the heap leaching costs to make the process feasible.

关键词： Diffusion-advection-reaction equations nonlinear problems Homotopy perturbation method finite volume method analytical solution Heap(bio)-leaching

Septic B-Spline Solution of Fifth-Order Boundary Value problems

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Journal of Applied Mathematics and Physics 2016年第8期4卷 1446-1454页

作者： Bin Lin School of Mathematics and Computation Science Lingnan Normal University Zhanjiang China

A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques.

关键词： Septic B-Spline Function Fifth-Order Boundary Value problems B-Spline Collocation Method nonlinear problems