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Scientific_Computing

FourierTransform_PDE

  • 给出了Fourier变换的推导以及在PDEs中的应用;

  • 给出了1+1维Heat方程和Wave方程的解推导和动画展示;

  • 给出了三维线图和surface图的示例;

  • 给出了三维动画展示,参考前面Fourier变换在PDE中的应用,可以很容易就推广到2+1维PDEs的动画实现;

  • 为了学习的便利,这里没有给出.py文件,而是直接给出了notebook。

Computing_Symbolically

  • 列出了handcalc库的一些简单使用,该库主要用于指定输出格式的设定;
  • 概要地探究了sympy符号库的一些特性,包括符号结构树,expand, factor, collect, cancel, simplify, limit, series, diff, integrate, solve, dsolve等;
  • 除此之外,sympy库还可用于statistics, physics, group theory, matrix/graph theory, number theory等很多学科的学习与研究中。

Computing_Numerically

  • 包括前向差分,后向差分,中心差分,Euler scheme, leapfrog,Crank-Nicolson scheme等,后面将会继续添加finite element, finite volume, ENO/WENO, spectral method等;
  • 符号/odeint/手写数值算法的误差比较,ODE/PDE(包括heat, wave, convection, Burgers等)的数值求解(ICs/BCs)。

program_Trefethen

  • 包含了Chebyshev谱方法等数值方法的简单实现
  • KdV的数值解
  • 这在Julia 1.0环境下测试通过,但目前在Julia 1.5环境下好多以前放在基本库环境中的函数都被修改或放在了具体的库中了,比如diagm等线性代数操作已经被放在了特定的LinearAlgebra库中,这些问题有时间会进行更新测试。

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