ELECTRICAL SIMULATOR FOR SOLVING LINEAR AND NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH AN ITERATIVE METHOD FOR REFINING APPROXIMATE SOLUTIONS.

Jack Gelfand, Herschel Albert Rabitz, Kenneth Steiglitz

Research output: Contribution to conferencePaper

Abstract

We have explored the use of DC network analyzers for the solution of steady state partial differential equations. These circuits can be used as computers where the topology of the computer is equivalent to the topology of the problem being solved. Network analyzers were used extensively in the past as modelling devices in Physics, Chemistry and Engineering Design. Recent advances in circuit design and packaging allow us to build network analyzer circuits that were not possible at that time. In particular, we have investigated the stability properties of circuits which serve as analogs for the linear wave equation where the operator is indefinite. We show that this stability behavior is similar to the behavior of iterative solutions for similar equations in numerical analysis. In addition, we have been investigating a method that incorporates analog and digital components in an iterative scheme similar to Newton's method and makes use of the best features of each.

Original languageEnglish (US)
Pages309-312
Number of pages4
StatePublished - Apr 1 1984

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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