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The Quarterly Journal of Mechanics and Applied Mathematics 1964 17(1):91-103; doi:10.1093/qjmam/17.1.91
© 1964 by Oxford University Press
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APPROXIMATE INVERSION OF A CLASS OF LAPLACE TRANSFORMS APPLICABLE TO SUPERSONIC FLOW PROBLEMS{dagger}

YUDELL L. LUKE

( Midwest Research Institute )

Solution of numerous applied problems requires the inversion of a Laplace transform which involves functions of hypergeometric type. An approximation procedure for inverting transforms of this kind is presented. The method inverts rational function approximations of these transcendents (see Luke (13)), and yields simple and useful expressions for the desired inverse functions. To illustrate the technique, we consider the solution of the wave equation with particular boundary conditions. The functions which arise have numerous applications in supersonic flow, acoustics and heat conduction. In the field of aerodynamics, these include the velocity field of a circular cylinder impulsively moved in the axial direction with constant axial force, the flow past quasi-cylindrical bodies, shock-body interference, wing body interference and the transient motion of a body of revolution in supersonic flow.


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