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

2016-09-02
Ali, Hamidoglu
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.
10th International Conference on Management Science and Engineering Management (ICMSEM)

Suggestions

On general form of the Tanh method and its application to nonlinear partial differential equations
Hamidoğlu, Ali (American Institute of Mathematical Sciences (AIMS), 2016-6)
The tanh method is used to compute travelling waves solutions of one-dimensional nonlinear wave and evolution equations. The technique is based on seeking travelling wave solutions in the form of a finite series in tanh. In this article, we introduce a new general form of tanh transformation and solve well-known nonlinear partial differential equations in which tanh method becomes weaker in the sense of obtaining general form of solutions.
On the solution of nonlinear algebraic equations following periodic forced response analysis of nonlinear structures using different nonlinear solvers
Kizilay, H. Sefa; Ciğeroğlu, Ender (2021-01-01)
In periodic forced response analysis of nonlinear structures, most of the time analytical solutions cannot be obtained due to the complex behavior of the nonlinearity and/or due to the number of nonlinear equations to be solved. Therefore, numerical methods are widely used. For periodic forced response analysis of nonlinear systems, generally Harmonic Balance Method (HBM) or Describing Function Method (DFM), which transform the nonlinear differential equations into a set of nonlinear algebraic equations, ar...
Analytical solutions of shallow-water wave equations
Aydın, Baran; Kanoğlu, Utku; Department of Engineering Sciences (2011)
Analytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis –long waves– over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, th...
Moving mesh discontinuous Galerkin methods for PDEs with traveling waves
UZUNCA, MURAT; Karasözen, Bülent; Kucukseyhan, T. (2017-01-01)
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the effi...
EXACT SPIN AND PSEUDO-SPIN SYMMETRIC SOLUTIONS OF THE DIRAC-KRATZER PROBLEM WITH A TENSOR POTENTIAL VIA LAPLACE TRANSFORM APPROACH
Arda, Altug; Sever, Ramazan (2012-09-28)
Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different p...
Citation Formats
H. Ali, “On General Form of Tanh Method and Its Application to Medical Problems,” Baku, AZERBAIJAN, 2016, vol. 502, p. 269, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63784.