Stability of Charlie's Method on Linear Heat Conduction Equation

Abstract

Kaedah tak tersirat sangat menarik dalam mendapatkan penyelesaian beza terhingga bagi persamaan terbitan separa kerana sifatnya yang ringkas. Akan tetapi batasan kestabilan yang teruk yang dialami oleh kaedah ini mele\-mah\-kan ciri ini. Suatu kaedah yang mempunyai sifat kestabilan yang lebih baik ialah kaedah Charlie. Rantau kestabilan bagi kaedah ini untuk persamaan haba matra satu dibincangkan di sini. Katakunci: kaedah tak tersirat; kaedah Charlie; peramal-pembetul; kestabilan. Explicit schemes are attractive for obtaining finite difference solutions to partial differential equations because of their simplicity. However this feature is undermined by the severe restriction on stability that the schemes suffer. One method that appears to have better stability properties is Charlie's method. The stability region of this method applied to a one-dimensional heat conduction equation is discussed in this article. Keywords: Explicit schemes; Charlie's method; predictor-corrector; stability.