New Successive Approximation Methods for Solving Strongly Nonlinear Jaulent-Miodek Equations

Abstract

In this paper, we propose two new techniques for solving system of nonlinear partial differential equations numerically, which we first combine Laplace transformation method into a successive approximation method. Second, we combine Padé [2,2] technique into the first proposed technique. To test the efficiency of our techniques, Jaulent-Miodek system was used, which contains partial differential equations and has strongly nonlinear terms. Experimental results revealed that the first proposed technique gives better results when the interval of t is small in terms of error approximation in tabular and graphical manners. Moreover, the results also demonstrated that the second proposed technique gives better results regardless of the given interval of t in terms of the least square errors.

Keywords

• Jaulent-Miodek
• Successive Approximation Method
• Laplace Transformation
• Padé Technique