A novel technique for solving Cauchy problem for the third-order linear dispersive partial differential equation

Abstract

To solve Cauchy problem for the third-order linear dispersive partial differential equation, the reduced differential transform (RDT) method is used. Without using any discretization or perturbation the technique gives analytical approximation in the form of rapidly convergent sequence with well-structured terms that can usually be expressed in a compact form. The efficiency and reliability of the method is demonstrated through a variety of homogeneous/ non-homogeneous, one-, two-, and three-dimensional model problems. Comparison of the results by RDT method and those obtained through variational iteration method (VIM) signifies that RDT method is more efficient and rapidly convergent. Moreover it is computationally an inexpensive method. Key words: Cauchy problem, dispersive partial differential equation, reduced differential transformation