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

The Degasperis-Procesi (DP) equation is solved numerically using the Quartic B-Spline Collocation Method (QBCM). The quartic B-spline function is used to set up the collocation method to solve the nonlinear DP equation. The quartic B-spline is applied as an interpolating function in the spatial dime...

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Bibliographic Details
Main Authors: Suseelan, Menaga, Ahmad, Azhar, Hamid, Nur Nadiah Abd, Ismail, Ahmad Izani Md
Format: Conference Proceeding
Language:English
Subjects:
B spline functions
Collocation methods
Finite difference method
Online Access:Get full text
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Summary:The Degasperis-Procesi (DP) equation is solved numerically using the Quartic B-Spline Collocation Method (QBCM). The quartic B-spline function is used to set up the collocation method to solve the nonlinear DP equation. The quartic B-spline is applied as an interpolating function in the spatial dimension while the Finite Difference method (FDM) is used to discretize the time derivative. The nonlinear DP equation is linearized using Taylor’s expansion and then the equation is discretized using the θ-weighted scheme. Crank-Nicolson and Implicit schemes are used. In order to demonstrate the capability of the schemes, two problems are solved and the solutions obtained are compared with the analytical solutions. The proposed numerical schemes are found to be in line with the analytical solutions.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5041613