Wavelet Method for Solving Cahn-Allen Equation

Abstract In this paper, we develop an accurate and efficient Haar wavelet method for well-known Cahn-Allen equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive

The first-integral method applied to the Eckhaus equation

AbstractThe first-integral method is a direct algebraic method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. In this work, we apply the first-integral method to study the exact solutions of the Eckhaus equation