NUMERICAL INVESTIGATION OF REGULARIZED LONG WAVE EQUATION USING HYBRID CUBIC B-SPLINE METHOD

Muhammad Wakeel; Muhammad Awais; Syed Sarmad Hasan

doi:10.71146/kjmr749

Authors

Muhammad Wakeel The Superior University Lahore, Pakistan. Author
Muhammad Awais The Superior University Lahore, Pakistan. Author
Syed Sarmad Hasan The Superior University Lahore, Pakistan. Author

DOI:

https://doi.org/10.71146/kjmr749

Keywords:

Regularized Long wave equation, Hybrid Cubic B-spline, Partial Differential Equations, Numerical Approximation, Finite Difference Scheme, Stability, Convergence

Abstract

The Regularized long wave equation (RLWE) is a significant nonlinear partial differential equation (PDE) which is extensively applied in various fields of applied mathematics including shallow water wave models and many other physical phenomena. This research aims to construct an efficient and accurate numerical technique based on Hybrid Cubic B-splines (HCBS) to find the approximate solution of Regularized long wave equation. There are very few analytical solutions to such nonlinear partial differential equations and so numerical approximations must be obtained through reliable numerical techniques. In the present research, HCBS functions are used to estimate the spatial derivatives of the RLWE and an appropriate finite difference scheme (FDS) is used for time discretization. This transforms the governing differential equation into a system of algebraic equations, which can then be solved numerically. Numerical experiments are carried out to evaluate the performance of the proposed algorithm in terms of accuracy, stability and efficiency. The obtained numerical results are found to be in good agreement with the exact solution which demonstrates that the proposed scheme is a good approximation with lower computational cost.

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