Modified Crank–Nicolson Scheme with Richardson Extrapolation for One-Dimensional Heat Equation

被引：0
作者：
Feyisa Edosa Merga
Hailu Muleta Chemeda
机构：
[1] Jimma University,Department of Mathematics
来源：
Iranian Journal of Science and Technology, Transactions A: Science | 2021年 / 45卷
关键词：
Heat equation; Modified Crank–Nicolson scheme; Order of convergence; Richardson extrapolation; Unconditionally stable;
D O I：
暂无
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学科分类号：
摘要：
In this paper, Modified Crank–Nicolson method is combined with Richardson extrapolation to solve the 1D heat equation. The method is found to be unconditionally stable, consistent and hence the convergence of the method is guaranteed. The method is also found to be second-order convergent both in space and time variables. When combined with the Richardson extrapolation, the order of the method is improved from second-to fourth-order. To validate the proposed method, two model examples are considered and solved for different values of spatial and temporal step lengths.
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页码：1725 / 1734
页数：9
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