Downloads: 111
Research Paper | Mathematics | Kenya | Volume 5 Issue 12, December 2016
Finite Difference Solution of (2+1)-Dimensional Sine-Gordon Equation: A Model for Investigating the Effects of Varying Surface Damping Parameter on Josephson Current Flowing through the Long Josephson Junction
Tinega Abel Kurura | Oduor Okoya [2] | Omolo Ongati [4]
Abstract: Modeling of some physical phenomena and technological processes taking into account dissipation leads to the Sine-Gordon equation with the first time derivative. The (2+1) Sine-Gordon equation with the first time derivative is used in explaining a number of physical phenomena including the propagation of fluxons in Josephson junctions. This study uses Finite Difference Method to solve (2+1) dimensional Sine-Gordon equation with the first time derivative that models dissipation of the current flow through the long Josephson junction. An Alternating Direction Implicit numerical scheme for the equation is developed with concepts of stability tested using Matrix Method. The value of surface damping parameter used are =1.1, =3.7, =7.2 and =9.3 for Alluminium (Al), Tin (Sn), Lead (Pb), and Niobium (Nb) respectively. The numerical results obtained are presented in tables and graphs. The computational results obtained indicate that as the length of long Josephson junction increases, the current flowing through the long Josephson junction decreases to zero. The results also indicate that when the surface damping parameter increases, the current flowing through the long Josephson junction also increases.
Keywords: Alternating Direction implicit Scheme, Finite Difference Method, Sine-Gordon Equation, Matrix Method, and Stability Analysis, Surface damping parameter, and Partial Differential Equation
Edition: Volume 5 Issue 12, December 2016,
Pages: 1249 - 1255
Similar Articles with Keyword 'Finite Difference Method'
Downloads: 0
Research Paper, Mathematics, Kenya, Volume 10 Issue 7, July 2021
Pages: 635 - 638Finite Difference Method Solution to Garlerkin's Finite Element Discretized Beam Equation
Downloads: 1 | Weekly Hits: ⮙1 | Monthly Hits: ⮙1
Analysis Study Research Paper, Mathematics, Kenya, Volume 12 Issue 10, October 2023
Pages: 1411 - 1416Numerical Modeling of Vibratory Motion of Shock Absorber Performance in Automobiles
Abel Kurura Tinega [3] | Omariba Geofrey Ong'era