An extension of Lagrange's method to certain systems of first order partial differential equations

Abstract

A modification of the method of characteristics has been developed to solve systems of first order hyperbolic partial differential equations where the characteristic curves are essentially identical. This method is applicable to fluid mixtures whose component fluid velocities are the same. Techniques were developed to find the solutions at desired points in space and time and to handle the conditions at the boundaries. Results of the application of this method to the solution of ion density distributions in the Earth's ionosphere are illustrated.