A new innovative stable time-dependent compressible flow solution over the order of nanoseconds is provided here for wide-ranging critically important challenging applications. Specifically, a solution of the highly complex unsteady high speed oscillating compressible flow field inside a cylindrical tube, closed at one end with a piston oscillating at very high resonant frequency at the other end, has been obtained numerically, assuming one dimensional, viscous, and heat conducting flow, by solving the appropriate fluid dynamic and energy equations. An iterative implicit finite difference scheme is employed to obtain the solution. The scheme permits arbitrary boundary conditions at the piston and the end wall and allows assumptions for tansport properties. In successfully predicting the time dependent results/data, an innovative simple but stable solution of unsteady fluid dynamic and energy equations is provided here for wide ranging research, design, development, analysis, and industrial applications in solving a variety of complex fluid flow heat transfer problems. The method is directly applicable to pulsed or pulsating flow and wave motion thermal energy transport, fluid-structure interaction heat transfer enhancement, nanoscale heat and mass transfer, diverse range of advanced fluidics, biofluidics / bioengineering, and fluidic pyrotechnic initiation devices. It can further be easily extended to cover muzzle blasts and high energy nuclear explosion blast wave propagations in one dimensional and/or radial spherical coordinates with or without including energy generation / addition terms.