Abstract
We extend Glimm's method for conservation laws to a larger class of sources so that it can be applied to the compressible Euler equations in transonic flow. Our approximate solutions to the Cauchy problem are constructed by combining the Glimm scheme with the splitting algorithm. We study the nonlinear interaction between wave patterns and the perturbations, and establish the stability of our scheme. Therefore, a more general Glimm-type argument is developed.
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