In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faste...

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...

We show the existence of at least one nontrivial solution for a nonlinear sixth-order ordinary differential equation is investigated. Our approach based on critical point theory.

in this work, byemploying the leggett-williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry alg...

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G′/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expr...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

This paper is devoted to introduce analytic solutions by Differential Transform Method-Pade approximants with theoretical study for the problem of the hydromagnetic flow due to a permeable stretching surface embedded in a porous medium in the presence of transverse magnetic field. The governing momentum equation which is a nonlinear partial differential equation is reduced into a nonlinear ordi...