Two unconditionally stable and convergent difference schemes with the extrapolation method for the one‐dimensional distributed‐order differential equations |
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| Authors: | Guang‐hua Gao Zhi‐zhong Sun |
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| Affiliation: | 1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, People's Republic of China;2. Department of Mathematics, Southeast University, Nanjing, People's Republic of China |
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| Abstract: | The Grünwald formula is used to solve the one‐dimensional distributed‐order differential equations. Two difference schemes are derived. It is proved that the schemes are unconditionally stable and convergent with the convergence orders  and  in maximum norm, respectively, where  and  are step sizes in time, space and distributed order. The extrapolation method is applied to improve the approximate accuracy to the orders  and  respectively. An illustrative numerical example is given to confirm the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 591–615, 2016 |
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| Keywords: | distributed‐order differential equations fractional derivative difference scheme extrapolation stability convergence |
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