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A high‐order compact scheme for the nonlinear fractional K lein– G ordon equation
Author(s) -
Vong Seakweng,
Wang Zhibo
Publication year - 2015
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.21912
Subject(s) - mathematics , nonlinear system , scheme (mathematics) , convergence (economics) , fractional calculus , order (exchange) , stability (learning theory) , mathematical analysis , computer science , physics , finance , quantum mechanics , machine learning , economics , economic growth
In this article, a high‐order finite difference scheme for a kind of nonlinear fractional Klein–Gordon equation is derived. The time fractional derivative is described in the Caputo sense. The solvability of the difference system is discussed by the Leray–Schauder fixed point theorem, while the stability and L ∞ convergence of the finite difference scheme are proved by the energy method. Numerical examples are provided to demonstrate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 706–722, 2015