Abstract
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.
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