Premium
Operator splitting for the fractional Korteweg‐de Vries equation
Author(s) -
Dutta Rajib,
Sarkar Tanmay
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22810
Subject(s) - mathematics , korteweg–de vries equation , commutator , operator splitting , operator (biology) , convergence (economics) , mathematical analysis , order (exchange) , godunov's scheme , pure mathematics , numerical analysis , lie algebra , physics , chemistry , biochemistry , lie conformal algebra , finance , repressor , quantum mechanics , nonlinear system , transcription factor , economics , gene , economic growth
Our aim is to analyze operator splitting for the fractional Korteweg‐de Vries (KdV) equation,u t = uu x + D α u x , α ∈ [ 1 , 2 ] , whereD α = − ( − Δ ) α / 2is a non‐local operator with α ∈ [ 1 , 2 ) . Under the appropriate regularity of the initial data, we demonstrate the convergence of approximate solutions obtained by the Godunov and Strang splitting. Obtaining the Lie commutator bound , we show that for the Godunov splitting, first order convergence inL 2is obtained for the initial data inH 1 + αand in case of the Strang splitting, second order convergence inL 2is obtained by estimating the Lie double commutator for initial data inH 1 + 2 α. The obtained rates are expected in comparison with the KdV( α = 2 )case.