Abstract
Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.
Highlights
Researchers in the past have worked on mathematical models explaining the behavior of a nonlinear wave phenomenon which is one of the significant areas of applied research
Qu and Wang [14] developed the alternating segment explicit-implicit (ASE-I) difference scheme consisting of four asymmetric difference schemes, a classical explicit scheme, and an implicit scheme, which is unconditionally linearly stable by the analysis of linearization procedure
Kolebaje and Oyewande [17] investigated the behavior of solitons generated from the KdV equation that depends on the nature of the initial condition, by using the Goda method [18], the Z-K method, and the Adomian decomposition method
Summary
Researchers in the past have worked on mathematical models explaining the behavior of a nonlinear wave phenomenon which is one of the significant areas of applied research. It is required to improve schemes that have a broad range of stability and high order of accuracy This leads to the solution of the system for linear. Many scientists concentrated upon the difference method that makes a discrete analogue effective in the fundamental conservation properties This causes us to create finite difference schemes which preserve the mass and energy of solutions for the KdV equation. Two fourth-order difference schemes are constructed for the one dimensional KdV equation: ut + αuxxx + γ (u2)x = 0, xL < x < xR, 0 ≤ t ≤ T, (1) with an initial condition u (x, 0) = u0 (x) , xL ≤ x ≤ xR,. We create fourth-order finite difference schemes for the KdV equation with the initial and boundary conditions. We finish our paper by conclusions in the last section
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
