Numerical Algorithms

, Volume 78, Issue 2, pp 485–511 | Cite as

A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations

Original Paper

Abstract

We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties for the analysis is that certain weight averages of the approximated solutions are considered in the discretization and standard energy estimates cannot be applied directly. By introducing a new grid function, which further approximates the solution, and using ideas in some recent studies, we show that the method converges with second-order accuracy in time.

Keywords

Linearized scheme Time fractional differential equations Nonlinear Klein-Gordon equations Convergence 

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Notes

Acknowledgment

The authors would like to thank the referees for their comments which improve the paper significantly. We also want to thank Prof. Honglin Liao for the helpful discussion on the estimates of Lemmas 2.2 and 2.3.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MacauMacauChina

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