Trinh @ Bath

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vpde_lecture22 [2020/03/26 13:29]
trinh 		vpde_lecture22 [2020/03/26 13:42] (current)
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 ====== MA20223 Lecture 22 ====== ====== MA20223 Lecture 22 ======
  
-//This lecture is about terminology but it is important not to be bogged down by terminology. You will practice by doing!// +//This lecture is about terminology but it is important not to be bogged down by terminology. You will practice by doing! This lecture covered part of **Chapter 15**.//
  
 +
 +<html>
 <iframe width="560" height="315" src="https://www.youtube.com/embed/30UzA62y_XE" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> <iframe width="560" height="315" src="https://www.youtube.com/embed/30UzA62y_XE" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
 +</html>
  
 ===== An example ===== ===== An example =====
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 where $b_n$ will be the Fourier sine coefficients of the odd $2\pi$ extension of $f(x)$ on $[0, \pi]$.  where $b_n$ will be the Fourier sine coefficients of the odd $2\pi$ extension of $f(x)$ on $[0, \pi]$. 
  
-<Code:Matlab linenums:1 |Solution of 1D heat equation with zero Dirichlet> +See the video for details of the calculation; we were not able to get to the end of the calculation by the lecture's end, but it will be simple for us to finish it all up in [[vpde_lecture23|MA20223 Lecture 23]]
-% Written for MA20223 Vectors & PDEs +
-clear           % Clear all variables +
-close all       % Close all windows +
- +
-N = 20;          % How many Fourier modes to include? +
- +
-% Define an in-line function that takes in three inputs:  +
-%   Input 1: n value [scalar] +
-%   Input 2: x value [vector] +
-%   Input 3: t value [scalar] +
-R = @(n, t, x) -2/(n*pi)*((-1)^n - 1)*exp(-n^2*t)*sin(n*x); +
- +
-% Create a mesh of points between two limits +
-x0 = pi; +
-x = linspace(0, x0, 1000); +
- +
-% Create a mesh of points in time +
-t = linspace(0, 5, 200); +
- +
-figure(1);                                  % Open the figure +
-plot([0, pi], [1, 1], 'b', 'LineWidth', 2); % Plot the base function +
-ylim([-0.2,1.2]);                           % Set the y limits +
-xlim([0, x0]);                              % Set the x limits +
-xlabel('x'); ylabel('u(x,t)'); +
-hold on +
-for j = 1:length(t) +
-    tj = t(j); +
-     +
-    u = 0; +
-    for n = 1:N +
-        u = u + R(n, tj, x); +
-    end +
-     +
-    % Plotting commands +
-    if j == 1 +
-        p = plot(x, u, 'r'); +
-    else +
-        set(p, 'YData', u); +
-    end +
-    drawnow +
-    title(['t = ', num2str(tj)]); +
-    pause(0.1); +
-    +
-    if j == 1 +
-        pause +
-    end +
-end +
-</Code>+
Last modified: 2020/03/26 13:29