Numerical Simulation of Dispersive Shallow Water Waves with an Efficient Method

Abstract

The main purpose of this paper has been to compare the numerical results when the septic B-spline is used in the collocation method, and performance of the splitting technique in the numerical methods has been investigated. So numerical solutions of the Rosenau-KdV equation have been constructed by using the collocation method with septic B-splines as interpolation functions. The Rosenau-KdV equation is split both in space and in time. Those coupled systems of differential equations are also solved by way of the septic B-spline collocation method over uniform finite intervals.

Numerical Solution of Schrödinger Equation by Crank–Nicolson Method

“…dinger equation has been solved by HWCM with stability analysis [24]. Different types of nonlinear equations are solved using the Kudryashov method [25] and quintic B-splines collocation methods [26][27][28][29] including fractional Schrödinger equations [30], which have importance in applied mathematics and optics.…”

Theoretical and Numerical Studies of Two Point Boundary Value Problems Using Trigonometric and Exponential Cubic B-Splines

“…where α (x) , β (x) and γ(x) are coefficients and g (x, V ) is forcing function. Cubic splines are used in [1][2][3][4][5][6][7][8] and B-splines as cubic, quintic and septic are presented in [9][10][11][12][13][14][15]. The trigonometric cubic B-spline is studied to solve numerical solutions of various partial differential equations [16][17][18][19][20].…”

Numerical Study of Rosenau-KDV Equation Using Finite Element Method Based on Collocation Approach

“…Different types of waves occur in nature having different kind of applications. Dynamics of shallow water waves that are observed along lake shores and beaches have been an active research area for the past few decades [1,2,8,9,22]. Specifically, the Korteweg-de Vries (KdV) equation U t + aU U x + bU xxx = 0 is a generic model for the study of nonlinear shallow water waves [10].…”