Super convergence analysis of fully discrete Hermite splines to simulate wave behaviour of Kuramoto-Sivashinsky equation

An improved collocation technique has been proposed to discretize the fourth-order multi-parameter non-linear Kuramoto-Sivashinsky (K-S) equation. The spatial direction has been discretized with quintic Hermite splines, whereas the temporal direction has been discretized with a weighted finite difference scheme. The fourth-order equation in space direction has been decomposed into second-order using space splitting by intro-ducing a new variable. Space splitting has been proposed to improve the convergence of the approximate solution. The proposed equation has been analyzed on a uniform grid in both space and time directions. Error bounds for general order Hermite splines are established for fully discrete scheme. Stability analysis for the proposed scheme has also been discussed elaborately. Periodic and non periodic problems of K-S equation type have been discussed to study the technique. The error growth has been addressed by computing L2- norm and L & INFIN;- norm. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

An improved collocation technique is proposed for discretizing the fourth-order multi-parameter non-linear Kuramoto-Sivashinsky (K-S) equation. Quintic Hermite splines are used to discretize the spatial direction, while a weighted finite difference scheme is used to discretize the temporal direction. The fourth-order equation in space direction is decomposed into second-order using space splitting, and the proposed equation is analyzed on a uniform grid in both space and time directions. Error bounds are established for general order Hermite splines, and stability analysis is discussed in detail. Periodic and non-periodic problems of K-S equation type are studied, and error growth is addressed by computing L2-norm and L∞-norm.