On General Form of Tanh Method and Its Application to Medical Problems


Hamidoğlu A.

Proceedings of the Tenth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing, Xu J.,Hajiyev A.,Nickel S.,Gen M., Editör, Springer, London/Berlin , Singapore, ss.269-278, 2016

  • Basım Tarihi: 2016
  • Yayınevi: Springer, London/Berlin 
  • Basıldığı Şehir: Singapore
  • Sayfa Sayıları: ss.269-278
  • Editörler: Xu J.,Hajiyev A.,Nickel S.,Gen M., Editör

Özet

The tanh method is used to compute travelling waves solutions of one-dimensional non-linear wave and evolution equations. The technique is based on seeking travelling wave solutions in the form of a finite series in tanh. However, the mentioned method is not always efficient method to solve some types of one dimensional non-linear partial differential equations in more general sense. In this article, we construct new general transformation of tanh function which is more effective in the sense of getting general solutions. By using our new transformation, we solved some important non-linear partial differential equations related with medicine, biology and physics. We examine Belousov–Habotinskii reaction which is often used to understand embryonic development and some of the complex wave behavior in the heart and other organs in the body, Fitzhugh–Nagumo equation which arises in population genetics and models the transmission of nerve impulses, and some other crucial non-linear partial differential equations applied in physics.