A novel convenient finite difference method for shallow water waves derived by fifth-order Kortweg and De-Vries-type equation

Abstract

In this research, two new finite difference schemes are derived and presented for estimating a solution to the fifth-order Kortweg and De-Vries equation. The global conservation law on any time–space regions which yields a three-level linear-implicit algorithm with a diagonal system is exactly preserved by the intended finite difference method. Theoretically verified and numerically proved, the created schemes are unconditionally stable and have the second-order accuracy both in time and space. The obtained results guarantee that the novel idea offers a new aspect to analyze the wave behavior.