Analog-Digital Methods of Solving Partial Differential Equations

摘要

Based on the success of analog techniques in solving ordinary differential equations and the high solution rate afforded by modern, wide bandwidth analog computers, detailed studies have been conducted on applying combined analog-digital techniques to the solution of partial differential equations. This final report summarizes the various methods investigated over a period of time, including the continuous time-discrete space approach; the continuous space-discrete time approach, block relaxation techniques, and the application of integral equations. The principal objectives have been to establish workable hybrid equipment and procedures for solving this class of problems and to compare these procedures to digital methods with respect to computation time, fidelity of solution, overall convenience and economy. Typical problems have been implemented to demonstrate each procedure. The emphasis in every case, however, has been on the methods used rather than on obtaining solutions for specific problems. Several dynamic studies of chemical processes that appear promising as hybrid applications are also discussed. (Author)