A solution of the highly complex unsteady high speed oscillating compressible flow field inside a cylindrical tube has been obtained numerically, assuming one dimensional, viscous, and heat conducting flow, by solving the appropriate fluid dynamic and energy equations. The tube is approximated by a right circular cylinder closed at one end with a piston oscillating at very high resonant frequency at the other end. 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 transport properties. The solution would also be valid for tapered tubes if the variations in the cross-sectional area are small. In successfully predicting the time dependent results, 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, and fluidic pyrotechnic initiation devices. It can further be easily extended to cover muzzle blasts and nuclear explosion blast wave propagations in one dimensional and/or radial spherical coordinates with or without including energy generation / addition terms.