New trigonometric B-spline approximation for numerical investigation of the regularized long-wave equation

Abstract

The objective of this work is to propose a collocation technique based on new cubic trigonometric B-spline (NCTB-spline) functions to approximate the regularized long-wave (RLW) equation. This equation is used for modelling numerous problems occurring in applied sciences. The NCTB-spline collocation method is used to integrate the spatial derivatives. We use the Rubin–Graves linearization technique to linearize the non-linear term. The accuracy and efficiency of the technique are examined by employing it on three important numerical examples which have three invariants of motion viz. mass, momentum, and energy. It is observed that the error norms of the present method are less than the error norms of the methods available in the literature. The numerical values of these invariants have also been approximated, which remain conserved during the program run which shows that the propagation of the solitary wave is represented perfectly. The propagation of one and two solitary waves and undulations of waves are depicted graphically. The stability analysis shows that the method is unconditionally stable.

Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

“…The implicit Crank -Nicolson method can be used to efficiently solve the heat equation [19,20]. Many authors [21][22][23][24][25] have used higher order B-splines such as quintic, quartic, sextet and septic B-splines for the solutions of different PDEs but faced computational higher cost. Also, Riccati matrix delay differential equations has solved with variational iteration method in these papers [26][27][28][29][30].…”

Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation

“…The BBME has been solved numerically by various methods based on finite difference, finite element, Petrov-Galerkin finite element, Fourier pseudo-spectral, collocation methods, and many other methods [4][5]. Lately, the B-spline collocation method with quadratic B-spline [4], cubic B-spline (CB) [6][7][8], cubic trigonometric B-spline (CTB) [9][10][11], and extended cubic B-spline (ECB) [12][13][14][15][16] have been formulated successfully on some differential equations with accurate results and high efficiency. There are several techniques used to handle the nonlinear term in the BBME namely Taylor series expansion [17], quasilinearization [18] and Adomian polynomials [19].…”