Higher order B‐spline differential quadrature rule to approximate generalized Rosenau‐RLW equation
Copyright policy )Higher order B‐spline differential quadrature rule to approximate generalized Rosenau‐RLW equation
In this article, B‐spline‐based collocation method is employed to approximate the usual and modified Rosenau‐RLW nonlinear equations. The weighted extended B‐spline (WEB‐spline) is used as the modified form of B‐spline as the usual B‐splines fail to obey the Dirichlet boundary conditions. The WEB method is more general method that allows to discretize the domain into finite number of elements not necessarily start from the boundary points of the domain. Our method omits the linearization process of the nonlinear partial differential equation (PDE). Different cases are discussed by setting the parameter p=2,3,4, and 6 that appears in Rosenau‐RLW equations. The error estimation is calculated, which gives good agreement of the exact solution.
- Prince Sattam Bin Abdulaziz University Saudi Arabia
- Salman bin Abdulaziz University Saudi Arabia
- JECRC University India
- University of Rajasthan India
- Islamia University of Bahawalpur Pakistan
WEB-spline, collocation method, Rosenau-RLW equation, KdV equations (Korteweg-de Vries equations), SSP-RK54 scheme, Thomas algorithm, Direct numerical methods for linear systems and matrix inversion, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Numerical computation using splines
WEB-spline, collocation method, Rosenau-RLW equation, KdV equations (Korteweg-de Vries equations), SSP-RK54 scheme, Thomas algorithm, Direct numerical methods for linear systems and matrix inversion, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Numerical computation using splines
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