Publish in OALib Journal
APC: Only $99
The ？exp(-j(x))？method is employed to find the exact traveling wave solutions involving parameters for nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the ？exp(-j(x))？？method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.
In this paper, we
propose and analyze some schemes of the integral collocation formulation based
on Legendre polynomials. We implement these formulae to solve numerically
Riccati, Logistic and delay differential equations with variable coefficients.
The properties of the Legendre polynomials are used to reduce the proposed
problems to the solution of non-linear system of algebraic equations using
Newton iteration method. We give numerical results to satisfy the accuracy and
the applicability of the proposed schemes.