[PDF] Top 20 Expanding the Tanh Function Method for Solving Nonlinear Equations

... KdV-Burgers equation in (34) and the Boussinesq equation in (49) which all give the exact solutions obtained before by the tanh-function method as a special cases [13-15]. Moreover, we discussed the ... See full document

... perturbation method and parameter expanding method are applied to the motion equations of two nonlinear ...for solving nonlinear equations and also can be used for ... See full document

... Halley method for solving the nonlinear ...the function, which is a serious drawback of these ...Halley method by replacing the second derivatives of the function by its finite ... See full document

... We generate (see [6]) a G/M/1 queueing system with the inter-arrival times density function a and the service times exp ( ) µ . We divide the simulation period t into m periods when we have no arrival and no ... See full document

... Abstract— In this paper, the tanh and Sech function methods are proposed to establish a traveling wave solution for nonlinear partial differential equations. The two methods are used to ... See full document

... the tanh-coth method and symbolic computation system Maple, we have obtained abundant new solutions of these ...the tanh-coth method is a powerful mathematical tool for solving ... See full document

... the nonlinear ordinary differential equations and partial differential equations are quite ...of nonlinear differential ...here: tanh − expansion method [ 1 ] − [ 7 ] , the ... See full document

... the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner ...The tanh-coth method proved ... See full document

... of nonlinear IE using Chebyshev basis and the method of collocation with Chebyshev ...This method had been used for systems of nonlinear IE ...Fredholm nonlinear integral ... See full document

... In this section, the obtained theoretical results are confirmed by numerical experiments. Numerical test re- sults are presented for the third-order method by com- parison with famous iterative methods of ... See full document

... y ′′′ = J y y y ′ ′′ (1) With initial conditions y ( ) 0 = 0, y ′ ( ) 0 = B y , ′′ ( ) 0 = 0 . The most general function of Jerk, which is invariant in time-reversal and space-reversal and only nonlinear ... See full document

... for solving nonlinear ...point method using taylor series on the functional equation x = g x ( ) of nonlinear equation f x ( ) = 0 ...original function f. In fixed point method, ... See full document

... procedure for the choice of the search direction (see[4, 5, 33]). Likewise, α k can be computed either exact or inexact. The most frequently used line search in practice is inexact line search [5, 10, 24] which is chosen ... See full document

... Y   aY  bY  c a  (2.4) where Y   d Y    d  . , , are constants to be determined later , and non-negative inte- gers and can be determined by considering the homogeneous balance between the highest order ... See full document

... rational hyperbolic and rational functions. The proposed method is powerful tool and very user-friendly for solving NLEEs. On exact solution some novel results and computational methods involved to ... See full document

... Newton’s method is simple to implement and has a quadratic rate of convergence, still it requires the computation and storage of n n  Jacobian matrix and its inverse, and also requires solving systems of ... See full document

... of function evaluations (NOFE) sufficient to meet the stopping ...order method of Fang for Fang and ...order method of Noor and al. method (algorithm ...Ham’s method (formula (10), ... See full document

... a nonlinear equation. The new Simpson-type method is shown to converge of the order ...new method requires the same amount of evaluations of the function and therefore the new method ... See full document

... valued function of the spatial coordinate 𝑥 and the time 𝑡, α and γ are positive real ...the nonlinear Schrodinger (NLS) and modified Korteweg-de Vries (mKdV) equations,as it is complex ... See full document

... phenomena. Nonlinear phenomena appear in a wide vari- ety of scientific applications such as plasma physics, solid state physics, fluid ...these nonlinear phenomena, many mathematicians and physical ... See full document