Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument

Abstract

We construct and investigate monotone and alternating rapidly convergent two-sided methods for the approximate integration of the generalized Goursat problem, prove the existence and uniqueness of its regular solution, establish theorems on differential inequality and comparison, and obtain sufficient conditions for the existence of solutions of the indicated problem of fixed sign in a given domain.