Practical Numerical Analysis (2021-22)

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  General

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  • Select activity Announcements

    

    Announcements Forum
• Select section Course Materials

  Course Materials

  • Select activity Sheet 1

    

    Sheet 1 Assignment

    Root-finding. The material for this sheet is contained in Lecture 1: Rootfinding.
  • Select activity Sheet 2

    

    Sheet 2 Assignment

    The \(\theta\)-method for initial value ODE problems. The material for this sheet is contained in Lecture 2: Initial Value Problems: ODEs.
  • Select activity Sheet 3

    

    Sheet 3 Assignment

    Runge-Kutta schemes for initial value ODE problems. The material for this sheet is contained in Lecture 3: Initial Value Problems: ODEs (question 1) and the first half of Lecture 4: Initial Value Problems: ODEs (question 2).
  • Select activity Sheet 4

    

    Sheet 4 Assignment

    Linear Multistep Methods. The material for this sheet is contained in the second half of Lecture 4: Initial Value Problems: ODEs.
  • Select activity Introduction to Practical Numerical Analysis

    

    Introduction to Practical Numerical Analysis File
  • Select activity Lecture 1: Rootfinding

    

    Lecture 1: Rootfinding File
  • Select activity bisect.m

    

    bisect.m File

    Matlab code for the bisection algorithm
    

  • Select activity newt.m

    

    newt.m File

    Matlab code for Newton's method in one space dimension
    

  • Select activity Lecture 2: Initial Value Problems: ODEs

    

    Lecture 2: Initial Value Problems: ODEs File

    The \(\theta\)-method for solving initial value ODE problems.
    

  • Select activity theta_method1.m

    

    theta_method1.m File

    Function to solve \(du/dt=\lambda u\) with \(u(0)=1\) using the theta method
    

  • Select activity example1.m

    

    example1.m File

    Runs the code theta_method1.m with a range of values for \(\lambda\) and numbers of timesteps to produce the plots for Example 1 in Lecture 2: Initial Value Problems: ODEs.
    

  • Select activity example2.m

    

    example2.m File

    Matlab script to produce the figures in Example 2 in Lecture 2: Initial Value Problems: ODEs.
    

  • Select activity Lecture 3: Initial Value Problems: ODEs

    

    Lecture 3: Initial Value Problems: ODEs File

    Runge-Kutta schemes for solving ODE initial value problems.
    

  • Select activity example1_rk.m

    

    example1_rk.m File

    Matlab code to solve the problem \(du/dt=\lambda u\) with \(u(0)=1\) using explicit Euler and improved Euler schemes as in Lecture 3: Initial Value Problems: ODEs.
    

  • Select activity example2_rk.m

    

    example2_rk.m File

    Code to generate the final figure in Lecture 3: Initial Value Problems: ODEs, illustrating convergence rates.
    

  • Select activity Lecture 4: Initial Value Problems: ODEs

    

    Lecture 4: Initial Value Problems: ODEs File

    Adaptive Runge-Kutta schemes and linear multistep methods
    

  • Select activity Lecture 5: 1D Parabolic PDEs: Finite Difference Methods

    

    Lecture 5: 1D Parabolic PDEs: Finite Difference Methods File
  • Select activity heat1d_explicit.m

    

    heat1d_explicit.m File

    Code to solve the heat equation using the explicit Euler scheme in time and central differences in space as described in Lecture 5: 1D Parabolic PDEs: Finite Difference Methods.
    

  • Select activity heat1d_theta.m

    

    heat1d_theta.m File

    Code to solve the heat equation using the \(\theta\)-method in time and central differences in space as described in Lecture 5: 1D Parabolic PDEs: Finite Difference Methods.
    

  • Select activity neumannbceg.m

    

    neumannbceg.m File

    Code to solve the heat equation with a Robin boundary condition using the \(\theta\)-method
    

  • Select activity neumannbc_conv.m

    

    neumannbc_conv.m File

    Use with neumannbceg.m. This code produces a convergence plot of the results of solving the heat equation with a Robin boundary condition using the \(\theta\)-method. We use two different second order approximations to the boundary condition.
    

  • Select activity Week 0 Matlab files

    

    Week 0 Matlab files