| 木材干燥过程中一个非线性模型的二阶收敛差分格式 |
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| 引用本文： | 姜明杰,孙志忠.木材干燥过程中一个非线性模型的二阶收敛差分格式[J].东南大学学报,2006,22(4):582-588. |
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| 作者姓名： | 姜明杰 孙志忠 |
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| 作者单位： | 东南大学理学院 南京210096 |
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| 基金项目： | The National Natural Science Foundation of China （No. 10471023）. |
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| 摘 要： | 针对描述木材干燥过程中的一个非线性微分方程模型,用降阶法对其建立了一个差分格式.此模型是由一个非线性常微分方程和一个非线性抛物方程组成的耦合微分方程组.首先引进一个新变量把原问题转化为一阶微分方程组问题,然后对此一阶微分方程组建立了一个线性化差分格式,应用能量方法证明了差分格式的可解性、稳定性和收敛性,并给出了误差估计式.差分格式关于时间步长和空间步长均为二阶.在实际计算时,将引入的新变量分离开,得到仅含原变量的差分格式,降低了计算量.数值计算结果验证了理论结果的可靠性.
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| 关 键 词： | 木材干燥过程 模型 非线性微分方程 差分格式 降阶法 稳定性 收敛性 |
| 收稿时间： | 10 26 2005 12:00AM |
Second-order difference scheme for a nonlinear model of wood drying process |
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| Jiang Mingjie,Sun Zhizhong.Second-order difference scheme for a nonlinear model of wood drying process[J].Journal of Southeast University(English Edition),2006,22(4):582-588. |
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| Authors: | Jiang Mingjie Sun Zhizhong |
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| Institution: | School of Sciences, Southeast University, Nanjing 210096, China |
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| Abstract: | A numerical simulation for a model of wood drying process is considered.The model is given by a couple of nonlinear differential equations.One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation.A difference scheme is derived by the method of reduction of order.First,a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations.Secondly,a difference scheme is constructed for the later problem. The solvability,stability and convergence of the difference scheme are proved by the energy method.The convergence order of the difference scheme is second-order both in time and in space.A prior error estimate is put forward.The new variable is put aside to reduce the computational cost.A numerical example testifies the theoretical result. |
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| Keywords: | wood drying process model nonlinear differential equation difference scheme method of reduction of order stability convergence |
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