Constructing analytic solutions on the Tricomi equation

Abstract

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Keywords

• homotopy analysis method (ham)
• variational iteration method (vim)
• square residual error
• auxiliary parameter
• lagrange multiplier
• 47.40.hg
• 47.40.ki