DİFÜZYON DENKLEMİNİN SINIRLAYICI TAYLOR YAKLAŞIMI YARDIMIYLA NÜMERİK ÇÖZÜMÜ

Yıl 2013, Sayı: 030, 9 - 15, 15.04.2013

Ahmet Boz

Öz

Bu çalışmada, lineer difüzyon denkleminin sınırlayıcı Taylor yaklaşımı yardımıyla nümerik çözümleri

elde edilmiştir. Difüzyon denkleminin nümerik çözümü için exp(xA) üstel matris yaklaşımı

kullanılmıştır. Bu yaklaşımın avantajı, bazı noktalarda denklemin tam değerine sahip olmasıdır. Difüzyon

denklemi için uygulanan yöntem sonucunda elde edilen veriler, yöntemin tutarlı olduğunu

göstermektedir.

Anahtar Kelimeler

Sınırlayıcı Taylor yaklaşımı, Difüzyon denklemi, sonlu farklar

NUMERICAL SOLUTION OF THE DIFFUSION EQUATION WITH RESTRICTIVE TAYLOR APPROXIMATION

Öz

In this paper, we solved linear diffusion equation using restrictive Taylor approximations. We use the

restrictive Taylor approximation to approximate the exponential matrix exp(xA) . The adventage is that

has the exact value at certain point. We will use a new technique for solution of the Diffusion equation.

The results show that the used numerical method produce the good results.

Anahtar Kelimeler

Restrictive Taylor approximation, Diffusion equation, Finite difference

Kaynakça

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