HYBRID QUINTIC B-SPLINE COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF THE BOUSSINESQ EQUATION

Fakhar Waqqas; Ayesha Tanveer; Tayyba Arif; Mehreen Zahid

doi:10.71146/kjmr691

Authors

Fakhar Waqqas The Superior University Lahore, Pakistan. Author
Ayesha Tanveer The Superior University Lahore, Pakistan. Author https://orcid.org/0009-0001-7244-2479
Tayyba Arif The Superior University Lahore, Pakistan. Author
Mehreen Zahid The Superior University Lahore, Pakistan. Author

DOI:

https://doi.org/10.71146/kjmr691

Keywords:

Boussinesq equation, Quintic B-spline collocation method, Hybrid scheme, Solitary waves, Von Neumann stability, Matrix system, Error bounds

Abstract

In this paper, a high-order Hybrid Quintic B-spline Collocation Method (HQBCM) is developed for the numerical solution of the non-linear Boussinesq equation governing non-linear dispersive wave propagation. By combining a second-order finite difference spatial hybrid scheme with fifth-degree B-spline basis functions across a spatial grid, the continuous governing partial differential equation is converted into an algebraic system of ordinary differential equations. Time integration is accomplished via a weighted θ-implicit scheme. Matrix formulation, von Neumann stability analysis, and global convergence bounds are rigorously presented. Three benchmark examples involving single solitary waves and interacting soliton collisions are solved to demonstrate the precision and conservation properties of the method.

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