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vpde_lecture22 [2020/03/24 15:27]
trinh
vpde_lecture22 [2020/03/26 13:42] (current)
trinh
Line 1: Line 1:
 ====== 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> 
 +</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 calculationwe were not able to get to the end of the calculation by the lecture's endbut 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>+