Improved wavelets based technique for nonlinear partial differential equations

One of the most challenging task now a days for engineers and scientists is finding solutions of nonlinear Partial Differential Equations (PDEs) which frequently arise in many engineering and physical phenomena’s. Encouraged by the ongoing research, a new technique is proposed in this article for obtaining more accurate results of nonlinear PDEs. Shifted Legendre wavelets and Picard’s Iteration Technique are used in the proposed technique. To test the significance of the proposed technique, nonlinear Gardner equation is considered and solved. The proposed technique provides very accurate results over a wider interval because of the use of the shifted polynomials. The results obtained are also compared with the results of Variational Iteration Method and the supremacy of the proposed method is established.