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具时间依赖边界条件的热传导方程近似解的精确性研究
Research on the Accuracy of Approximate Solution of the Heat Equation with Time-dependent Boundary Conditions
【摘要】 研究了求解具时间依赖边界条件的热传导方程的近似解的精确性.首先,对温度边界条件为时间的幂函数的情况,采用标准的多项式温度近似函数,对已有方法进行改进,即将多项式温度近似函数的指数由整数形式推广为非整数形式,从而提高温度近似解函数的精确性.然后,对复杂的时间依赖的边界条件,应用微分方程叠加原理,构建近似解表达式.实验结果显示,这种方法提高了计算精确性,改进了已有方法.
【Abstract】 The paper studies the accuracy of approximate solution of the heat equation with time-dependent boundary conditions. Firstly,when the temperature boundary condition is the power function of time,the standard polynomial approximation solution to the heat equation is adopted. To improve the existing methods,that is,the polynomial approximation function of temperature index extends from non integer form,so as to improve the accuracy of the approximation function of temperature. Secondly,the complex time dependent boundary condition is considered. Approximate solution expression is constructed by using the principle of superposition of linear differential equation. The experimental results show that this method improves the computational accuracy and improves the existing methods.
【Key words】 heat balance integral method; time-dependent boundary condition; Approximate solution; accuracy;
- 【文献出处】 许昌学院学报 ,Journal of Xuchang University , 编辑部邮箱 ,2017年05期
- 【分类号】O175
- 【下载频次】187