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A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes
Yanzhi, Liu Roberts, Jason A. Yan, Yubin
Yanzhi, Liu
Roberts, Jason A.
Yan, Yubin
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2017-10-09
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Abstract
We consider finite difference methods for solving nonlinear fractional differential equations in the Caputo fractional derivative sense with non-uniform meshes. Under the assumption that the Caputo derivative of the solution of the fractional differential equation is suitably smooth, Li et al. \lq \lq Finite difference methods with non-uniform meshes for nonlinear fractional differential equations\rq\rq, Journal of Computational Physics, 316(2016), 614-631, obtained the error estimates of finite difference methods with non-uniform meshes. However the Caputo derivative of the solution of the fractional differential equation in general has a weak singularity near the initial time. In this paper, we obtain the error estimates of finite difference methods with non-uniform meshes when the Caputo fractional derivative of the solution of the fractional differential equation has lower smoothness. The convergence result shows clearly how the regularity of the Caputo fractional derivative of the solution affect the order of convergence of the finite difference methods. Numerical results are presented that confirm the sharpness of the error analysis.
Citation
Yanzhi, L., Roberts, J., & Yan, Y. (2018). A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes. International Journal of Computer Mathematics, 95(6-7), 1151-1169. http://dx.doi.org/10.1080/00207160.2017.1381691
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Taylor & Francis
Journal
International Journal of Computer Mathematics
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DOI
10.1080/00207160.2017.1381691
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Article
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en
Description
This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on 09/10/2017, available online: http://dx.doi.org/10.1080/00207160.2017.1381691
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1029-0265