An approximation of the analytic solution of the shock wave equation

In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 ⩽ t < ∞ . Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.