Abstract
In this paper, two alternating direction implicit Galerkin-Legendre spectral methods for distributed-order differential equation in two-dimensional space are developed. It is proved that the schemes are unconditionally stable and convergent with the convergence orders O(Δt + σ2 + N−m) and O(Δt2 + σ2 + N−m), respectively, where Δt, σ, N, and m are the time step size, step size in distributed-order variable, polynomial degree, and regularity in the space variable of the exact solution, respectively. Moreover, the applicability and accuracy of the two schemes are demonstrated by numerical experiments to support our theoretical analysis.
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The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us improved the results of this paper.
Funding
The first and second authors are partially supported by theNational Natural Science Foundation of China Grant No. 11671233. The authors X. Li and Z. Liu thank for the financial support from China Scholarship Council.
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Li, X., Rui, H. & Liu, Z. Two alternating direction implicit spectral methods for two-dimensional distributed-order differential equation. Numer Algor 82, 321–347 (2019). https://doi.org/10.1007/s11075-018-0606-z
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DOI: https://doi.org/10.1007/s11075-018-0606-z