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High‐order difference scheme for the solution of linear time fractional klein–gordon equations
Author(s) -
Mohebbi Akbar,
Abbaszadeh Mostafa,
Dehghan Mehdi
Publication year - 2014
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.21867
Subject(s) - mathematics , discretization , dissipative system , fractional calculus , convergence (economics) , partial differential equation , mathematical analysis , order (exchange) , scheme (mathematics) , stability (learning theory) , derivative (finance) , physics , finance , quantum mechanics , machine learning , computer science , financial economics , economics , economic growth
In this article, we apply a high‐order difference scheme for the solution of some time fractional partial differential equations (PDEs). The time fractional Cattaneo equation and the linear time fractional Klein–Gordon and dissipative Klein–Gordon equations will be investigated. The time fractional derivative which has been described in the Caputo's sense is approximated by a scheme of order O ( τ 3 − α ) , 1 < α < 2 , and the space derivative is discretized with a fourth‐order compact procedure. We will prove the solvability of the proposed method by coefficient matrix property and the unconditional stability andL ∞ ‐convergence with the energy method. Numerical examples demonstrate the theoretical results and the high accuracy of the proposed scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1234–1253, 2014