Wave problem arises in various phenomena of science and engineering. This study proposes an efficient and appropriate scheme to produce the approximate solutions of multidimensional problems arising in wave propagation. We use a new iterative strategy (NIS) to minimize the computational cost and less time than other approaches studied in the literature. Since the variational iteration method (VIM) has some assumptions and restrictions of variables during the construction of the recurrence relation, we present a Sawi integral transform for the construction of the recurrence to overcome this difficulty. The series solution for this recurrence relation is determined using the homotopy perturbation strategy (HPS) in the form of convergence that provides the precise solution after a few iterations. This NIS does not require any discretization in the findings of results and derives the algebraic equations. Some numerical models and graphical representations are illustrated to verify the performance of this scheme.