Numerical Approximation for 2-Dimensional Schrödinger Equation Using Modified Gauss Elimination Method

Öz

In this study, modifed Gauss elimination method will be used to obtain solution of first order Rothe difference scheme and second order Crank-Nicholson difference scheme for numerical approximation of two-dimensional Schrödinger equation in space variable. One example is given and approximate solution is found by three methods. Modified Gauss elimination method is used with respect to time variable and with respect to space variable. In order to compare the difference schemes are also solved by the classical inverse matrix method.

Anahtar Kelimeler

• Modified Gauss elimination method
• Rothe difference scheme
• Self-adjoint operator

Modifiye Gauss Eleme Yöntemi Kullanarak 2-Boyutlu Schrödinger Denklemine Sayısal Yaklaşım

Öz

Bu çalışmada, uzay değişkeninde iki boyutlu Schrödinger denkleminin sayısal yaklaşımı için birinci mertebeden Rothe fark şemasının ve ikinci mertebeden Crank-Nicholson fark şemasının çözümünü elde etmek için modifiye Gauss eliminasyon yöntemi kullanılmıştır. Bir örnek verilmiş ve üç yöntemle yaklaşık çözüm bulunmuştur. Modifiye Gauss eliminasyon yöntemi, zaman değişkenine ve uzay değişkenine göre kullanılmıştır. Karşılaştırma yapmak için fark şemaları, klasik ters matris yöntemi ile de çözülmüştür.

Anahtar Kelimeler

• Modifiye Gauss eleme metodu
• Rothe fark şeması
• Öz-eşlenik operator

Kaynakça

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