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Research on Teaching Design of Numerical Analysis Course for Engineering Graduate Students
DOI: 10.12677/CES.2020.86185, PDF, HTML, XML, 下载: 530  浏览: 835  科研立项经费支持

Abstract: This paper mainly discusses how to design the teaching case of numerical analysis course for graduate students and its importance. In this process, students are guided to explore their think-ing, constantly discover new problems and analyze and solve them step by step, so that students can learn the basic methods of numerical analysis in the process of finding solutions and discussing solutions to problems, understand the core idea of numerical analysis, experience the core idea of numerical analysis, and cultivate innovative applied talents with the ability to propose, analyze and solve problems.

1. 研究背景

2. 案例设计教学过程

1) 提出问题

$\left\{\begin{array}{c}-\left(\frac{{\partial }^{2}u}{\partial {x}^{2}}+\frac{{\partial }^{2}u}{\partial {y}^{2}}\right)=f\left(x,\text{\hspace{0.17em}}y\right),\text{\hspace{0.17em}}0

2) 探究学习

$\begin{array}{l}4{u}_{i,j}-{u}_{i-1,j}-{u}_{i+1,j}-{u}_{i,j-1}-{u}_{i,j+1}={h}^{2}{f}_{ij}\begin{array}{c},\end{array}\text{\hspace{0.17em}}1\le i,\text{\hspace{0.17em}}j\le N,\\ {u}_{0,j}={u}_{N+1,j}={u}_{i,0}={u}_{i,N+1}=0.\end{array}$

$\begin{array}{l}\left({x}_{1},\text{\hspace{0.17em}}{y}_{1}\right),\text{\hspace{0.17em}}\left({x}_{2},\text{\hspace{0.17em}}{y}_{1}\right),\text{\hspace{0.17em}}\cdots ,\text{\hspace{0.17em}}\left({x}_{N},\text{\hspace{0.17em}}{y}_{1}\right),\text{\hspace{0.17em}}\left({x}_{1},\text{\hspace{0.17em}}{y}_{2}\right),\text{\hspace{0.17em}}\left({x}_{2},\text{\hspace{0.17em}}{y}_{2}\right),\\ \cdots ,\text{\hspace{0.17em}}\left({x}_{N},\text{\hspace{0.17em}}{y}_{2}\right),\text{\hspace{0.17em}}\cdots ,\text{\hspace{0.17em}}\left({x}_{1},\text{\hspace{0.17em}}{y}_{N}\right),\text{\hspace{0.17em}}\left({x}_{2},\text{\hspace{0.17em}}{y}_{N}\right),\text{\hspace{0.17em}}\cdots ,\text{\hspace{0.17em}}\left({x}_{N},\text{\hspace{0.17em}}{y}_{N}\right).\end{array}$

${u}_{i,j}^{\left(k+1\right)}=\left({u}_{i-1,j}^{\left(k+1\right)}+{u}_{i+1,j}^{\left(k\right)}+{u}_{i,j-1}^{\left(k+1\right)}+{u}_{i,j+1}^{\left(k\right)}+{h}^{2}{f}_{ij}\right)/4$

${u}_{i,j}^{\left(k+1\right)}=\left({u}_{i-1,j}^{\left(k\right)}+{u}_{i+1,j}^{\left(k\right)}+{u}_{i,j-1}^{\left(k\right)}+{u}_{i,j+1}^{\left(k\right)}+{h}^{2}{f}_{ij}\right)/4$

3) 推广应用

4) 归纳总结

3. 结语

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