Year: 2025
Type: article
Abstract: ABSTRACT In this paper, we study the stability and convergence of a conservative Crank–Nicolson finite difference scheme applied to the Korteweg–de Vries (KdV) equation endowed with initial data. We design a three‐point average scheme associated with the convective term, and the dispersion term is discretized by certain discrete operators along with the Crank–Nicolson scheme for the temporal discretization to establish that the proposed scheme is conservative. The convergence analysis reveals that utilizing inherent Kato's local smoothing effect , the proposed scheme converges to a classical solution for sufficiently regular initial data and to a weak solution in for nonsmooth initial data . Optimal convergence rates in both space and time for the devised scheme are derived. The theoretical results are justified through several numerical illustrations.
Authors: Mukul Dwivedi, Tanmay Sarkar
Institution: Indian Institute of Technology Jammu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $5,000
OpenAlex ID: W4412956694