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Unconditional error analysis of the linearized transformed L 1 virtual element method for nonlinear coupled time-fractional Schrödinger equations

Authors:

Jixiao GuoAuthors Info & Claims

Volume 457, Issue C

https://doi.org/10.1016/j.cam.2024.116283

Published: 15 March 2025 Publication History

Abstract

This paper constructs a linearized transformed L 1 virtual element method for the generalized nonlinear coupled time-fractional Schrödinger equations. The solutions to such problems typically exhibit singular behavior at the beginning. To avoid this pitfall, we introduce an identical s-fractional differential system derived from a smoothing transformation of variables t = s 1 / α, 0 < α < 1. By utilizing the discrete complementary convolution kernels, we prove the boundedness and error estimates of the solution of time-discrete system. Moreover, the unconditionally optimal error bounds of the proposed fully discrete scheme are derived in L 2-norm without restriction on the grid ratio. Finally, numerical tests on a set of polygonal meshes are presented to verify the theoretical results.

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Index Terms

Unconditional error analysis of the linearized transformed L 1 virtual element method for nonlinear coupled time-fractional Schrödinger equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Interpolation
      2. Numerical differentiation
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Error-correcting codes

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 457, Issue C

Mar 2025

1225 pages

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Copyright © 2024.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 15 March 2025

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