In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as mul...In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as multistage HAM （MSHAM）. HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analyti- cal work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge-Kutta （RK4） method.展开更多
In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative ...In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.展开更多
文摘In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as multistage HAM （MSHAM）. HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analyti- cal work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge-Kutta （RK4） method.
文摘In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.
