Preliminary investigation of a hybrid method for solving partial differential equations

In the digital computer solution of a partial differential equation involving both time and spatial variables the partial differential equation is approximated by difference equations arising from the discretization of both the time and spatial variables. The number of difference equations equals the number of spatial mesh points or stations times the number of time increments. In the analog computer solution of a partial differential equation the equation may be approximated by a set of coupled ordinary differential equations, one equation for each station. The set of differential equations is then solved simultaneously. Unless the problem is simple and the number of stations is small, digital computation may take a long time and analog computation may involve much equipment. The present investigation is an attempt to indicate a profitable way to solve partial differential equations with hybrid computation, using only a limited number of high speed analog components for integration and employing the digital computer for function storage and playback.