In this paper,we have proposed a time marching intregral equation method which does nothave the limitation of the time linearized integral equation method in that the latter method can not satisfac-torily simulate the shock-wave motions.Firstly,a model problem——one dimensional initial and boundaryvalue wave problem is treated to clarify the basic idea of the new method.Then the method is implementedfor 2-D and 3-D unsteady transonic flow problems.The introduction of the concept of a qua-si-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheetcondition.The numerical calculations show that the method is reasonable and reliable.
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