A consideration on the solution of partial differential equations by analog computer

Abstract

When solving partial differential equations with an analog computer, they are usually transformed first to difference equations. This transformation causes truncation errors because of the finite number of sections. In this paper, a method is proposed whereby two solutions involving trun cation errors are extrapolated to find the true solution. The proposed extrapolation formula is based on the fact that the error in the solution is approximately proportional to the square of the section length. It is a quite simple method and has a wide area of application. Application to the diffusion equation resulted in good accuracy. The method is shown to be effective in estimating the error and the optimum number of sections in a traditional dif ference equation solution.