New approximate-analytical solutions to partial differential equations via auxiliary function method

In this article, the optimal auxiliary function method (OAFM) is extended to general partial differential equations (PDEs). Our proposed method is highly efficient and provides the means of controlling the approximate solution's convergence. Illustrative examples are provided to prove the exceptional consistency of the PDEs’ analytical and numerical solutions. OAFM is practically very effective where with only one iteration, a very fast convergence is guaranteed. OAFM is considered a reliable and efficient technique with a high accuracy in finding solutions for such interesting problems while saving both volume and time in comparison to other related analytical techniques.