Abstract
The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. A comparison between the two schemes has been made and the results were found to be : the first scheme is simpler and has faster convergence while the second scheme is more accurate . Also , the stability analysis of the two methods by the use of Fourier (Von Neumann) method has been done and the results were found to be : The explicit scheme is conditionally stable if and the Crank–Nicholson is unconditionally stable .
Highlights
The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme.
إذ حبدئق أن الطريقدة الأولدى ميدطقر علدى نحدو، Fourier (Von Neumann) تاسدطرمام نريقدة
عنمما حنون f (u) = uا ن المعا لة ( )1سوف حطحو إلى معا لة Klein–Gordonالرطية إذ
Summary
The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. إذ حبدئق أن الطريقدة الأولدى ميدطقر علدى نحدو، Fourier (Von Neumann) تاسدطرمام نريقدة عنمما حنون f (u) = uا ن المعا لة ( )1سوف حطحو إلى معا لة Klein–Gordonالرطية إذ حنون f (u) = sin uاان المعا لة ( )1سوف حطحو إلى معا لة ]12[ Sine–Gordon
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