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Numerical analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

Numerical Mathematics(Theory,Methods and Applications) 2021年第1期14卷 71-112页

作者： Junying Cao Zhenning Cai School of Data Science and Information Engineering Guizhou Minzu University550025 GuiyangChina Department of Mathematics National University of SingaporeSingapore 119076Singapore

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo *** method is developed by dividing the domain into a number of subintervals,and applying the quadratic interpolation on each *** method is shown to be unconditionally stable,and for general nonlinear equations,the uniform sharp numerical order 3−νcan be rigorously proven for sufficiently smooth solutions at all time *** proof provides a gen-eral guide for proving the sharp order for higher-order schemes in the nonlinear *** numerical examples are given to validate our theoretical results.

关键词： Caputo derivative fractional ordinary differential equations high-order numerical scheme stability and convergence analysis

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ADI-FDTDMethod for Two-Dimensional Transient Electromagnetic Problems

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Communications in Computational Physics 2016年第1期19卷 94-123页

作者： Wanshan Li Yile Zhang Yau Shu Wong Dong Liang School of Mathematics Shandong UniversityJinan 250199P.R.China Department of Mathematical and Statistical Sciences University of AlbertaEdmontonABT6G 2G1Canada Department of Mathematics and Statistics York UniversityTorontoONM3J 1P3Canada

An efficient and accurate numerical scheme is proposed for solving the transverse electric(TE)mode electromagnetic(EM)propagation problemin two-dimensional *** scheme is based on the alternating direction finite-difference time-domain(ADI-FDTD)*** the conventional upward continuation approach for the earth-air interface,an integral formulation for the interface boundary is developed and it is effectively incorporated to the ADI *** and convergence analysis together with an error estimate are *** simulations are carried out to validate the proposed method,and the advantage of the present method over the popular Du-Fort-Frankel scheme is clearly *** of the electromagnetic field propagation in the ground with anomaly further verify the effectiveness of the proposed scheme.

关键词： ADI-FDTD interface boundary stability and convergence analysis

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A numerical framework for the approximate solution of fractional tumor-obesity model

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第1期10卷 106-118页

作者： Sadia Arshad Dumitru Baleanu Ozlem Defterli Shumaila Department of Mathematics COMSATS University Islamabad LahorePunjab 54000Pakistan Department of Mathematics and Computer Sciences Cankaya University Ankara 06530Turkey

In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).stability and convergence of the proposed schemes using Caputo and CF fractional operators are *** simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized *** perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.

关键词： Tumor-obesity model numerical approximation stability and convergence analysis

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