Numerical solution of the Degasperis-Procesi equation using the quartic B-spline collocation method

2018 ◽  
Author(s):  
Menaga Suseelan ◽  
Azhar Ahmad ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method

scholarly journals Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spline Collocation ◽  
Sine Gordon Equation ◽  
B Spline ◽  
Spline Collocation Method ◽  
B Splines ◽  
Spline Basis ◽  
The Given

Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

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