Numerical solution and stability analysis of the Sine-Gordon system in two dimensions | Zendy

Saad Manna | Zendy; Haneen Jassim | Zendy

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Numerical solution and stability analysis of the Sine-Gordon system in two dimensions

Author(s) -

Saad Manna,

Haneen Jassim

Publication year - 2012

Publication title -

maǧallaẗ al-rāfidayn li-ʿulūm al-ḥāsibāt wa-al-riyāḍiyyāẗ/al-rafidain journal for computer sciences and mathematics

Language(s) - English

Resource type - Journals

eISSN - 2311-7990

pISSN - 1815-4816

DOI - 10.33899/csmj.2012.163684

Subject(s) - von neumann stability analysis , stability (learning theory) , mathematics , sine , numerical analysis , sine wave , mathematical analysis , fourier transform , alternating direction implicit method , finite difference method , sine gordon equation , von neumann architecture , numerical stability , computer science , physics , geometry , nonlinear system , pure mathematics , soliton , voltage , machine learning , quantum mechanics

This paper deals with the numerical solution for Sine-Gordon system in two dimensions using two finite difference methods the (ADE) and (ADI) methods .A comparison between the two methods has been done and we have obtained that the (ADE) method is the easer while the (ADI) method is more accurate than the (ADE) method. We also studied the stability analysis for each method by using Fourier (Von Neumann) method and we have obtained that the (ADI) method is unconditionally stable while the (ADE) method is stable under the condition 2 2 2 1 c r and 2 1 2 r where 2 c is the ratio of the waves speed u , w and ( ) ( ) 2 2 x t r = .

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