ABSTRACT
The development of linear partial differential equations is characterized by the efforts to develop the general theory and various methods of solutions of linear equations. This chapter presents variational iteration method (VIM) and the Haar wavelet method to compute approximate analytical as well as numerical solutions of nonlinear partial differential equations. It consideres some specific nonlinear partial differential equations like Burgers' equation, the modified Burgers' equation, the Huxley equation, the Burgers–Huxley equation, and the modified Korteweg–de Vries equation, which have a wide variety of applications in physical models. The Haar wavelet method consists of reducing the problem to a set of algebraic equations by expanding the term, which has maximum derivatives, given in the equation as Haar functions with unknown coefficients. The operational matrix of integration is utilized to evaluate the coefficients of Haar functions. The main advantages of the proposed scheme are its simplicity, applicability, and less computational errors.
