Abstract
In the practical solution of partial differential equations, very high accuracy is sometimes needed, particularly when the derivatives of the solution are the quantities in which we are interested. A procedure is given here for obtaining this high accuracy by a combined numerical and electric resistor-network method. The equation is first solved approximately on the resistor network; then the residuals in the corresponding finite-difference equation are evaluated numerically. These residuals are used as current inputs to the nodes of the network to obtain a correction to the first solution. If the errors in the first solution (including both experimental and lumping errors) are of the order of a few per cent, then the errors in the corrected solution will be of the order of a few hundredths of 1 per cent. The method makes possible accurate solutions without very stringent requirements on the precision of the resistors and other components of the electric circuit.
