A hybrid method for the solution of first order partial differential equations arising in non-linear estimation

A method for the hybrid computer solution of the Cauchy problem for a general first order partial differential equation is presented. The method is based on the well known theory of characteristics and the solution is obtained by generating the characteristic curves of the partial differential equation. The problem is thus transformed to that of integrating a system of ordinary differential equations using different initial conditions. The organization of the computation is such that the analog computer integrates the system of ordinary differential equations whereas the digital computer commands the operation, supplies initial conditions and stores the results. The method has been illustrated by simulating two partial differential equations arising in non-linear estimation.