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2017•arXiv (Cornell University)Open access

A time-spectral algorithm for fractional wave problems

Binjie Li, Hao Luo, Xiaoping Xie

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Abstract

This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence of this algorithm are derived, and numerical experiments are performed, demonstrating the exponential decay in the temporal discretization error provided the solution is sufficiently smooth.

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What this paper is about

This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence of this algorithm are derived, and numerical experiments are performed, demonstrating the exponential decay in the temporal discretization error provided the solution is sufficiently smooth.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence of this algorithm are derived, and numerical experiments are performed, demonstrating the exponential decay in the temporal discretization error provided the solution is sufficiently smooth.

Key concepts: Discretization, Temporal discretization, Convergence (economics), Stability (learning theory), Exponential function, Discretization of continuous features, Algorithm, Discretization error

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