The Serial Solution of theDiffusion Equation Using NonstandardHybrid Techniques
Shu-Kwan Chan · 1969
In theconventional approach totheserial solution of theone-dimension diffusion equation usingcontinuous space- discrete time(CSDT)techniques, there isalarge amountofpositive feedback intheresultant analog programming. Forallpractical purposes, thepresence ofthis positive feedback makestheconven- tional analog methoduseless. Inthis paper, anewdirection ofattack isproposed utilizing the equivalence between theordinary differential equation andthecor- responding integral equation. Theapplication ofthis technique totwo demonstration problems, though relatively simple ones, isentirely satisfactory. Furthermore, themethoddemonstrated herecanbe applied tosituations wherethecoefficient ofthediffusion equation is aspatial function. Attheendofthereport, abrief discussion isalso given onpossible modifications tothetechnique used,soasto shorten thesolution time. IndexTerms-Continuous space-discrete timesolution, heat equation, instability, integral equation, modified Neumannseries, partial differential equation, variable coefficients.