Unconditionally Stable High Accuracy Alternating Difference Parallel Method for the Fourth-order Heat Equation
In this paper, we present a highly accurate alternating parallel difference method which solves the fourth-order heat equation subject to specific initial and boundary conditions. Based on a group of new Saul'yev type asymmetric difference schemes and the Crank-Nicolson scheme for the fourth-or...
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| Vydáno v: | Engineering letters Ročník 28; číslo 1; s. 56 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Hong Kong
International Association of Engineers
22.02.2020
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| ISSN: | 1816-093X, 1816-0948 |
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| Abstract | In this paper, we present a highly accurate alternating parallel difference method which solves the fourth-order heat equation subject to specific initial and boundary conditions. Based on a group of new Saul'yev type asymmetric difference schemes and the Crank-Nicolson scheme for the fourth-order heat equation, we derive a high-order, unconditionally stable and intrinsic parallel difference method. We also give the existence and uniqueness, the stability and the error estimate of numerical solution for the alternating difference parallel method. Theoretical analysis demonstrates that this method have obvious parallelism, unconditional stability and fourthorder convergence in space. Numerical experimentations are also conducted to compare the new method with the existing method. |
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| AbstractList | In this paper, we present a highly accurate alternating parallel difference method which solves the fourth-order heat equation subject to specific initial and boundary conditions. Based on a group of new Saul'yev type asymmetric difference schemes and the Crank-Nicolson scheme for the fourth-order heat equation, we derive a high-order, unconditionally stable and intrinsic parallel difference method. We also give the existence and uniqueness, the stability and the error estimate of numerical solution for the alternating difference parallel method. Theoretical analysis demonstrates that this method have obvious parallelism, unconditional stability and fourthorder convergence in space. Numerical experimentations are also conducted to compare the new method with the existing method. |
| Author | Guo, Geyang Zhai, Yishu |
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| SubjectTerms | Boundary conditions Stability analysis Thermodynamics |
| Title | Unconditionally Stable High Accuracy Alternating Difference Parallel Method for the Fourth-order Heat Equation |
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