Updated readme

HW6Problem2.m

@@ -7,7 +7,6 @@
 set(0, 'defaultAxesFontsize', 16)
 set(0, 'defaultTextFontsize', 16)
 set(0, 'defaultLineLineWidth', 2)
-hold on
 t = [0:dt:3]';
 y_n = zeros(size(t));
 y_n(1) = 1; %initial condition
@@ -18,12 +17,12 @@
 plot(t, y_analytical(t), 'k-', t, y_n, 'o-');
 title('Analytical vs. Euler')
 legend('Analytical', 'Euler', 'Location', 'Northeast')
-saveas(a, 'euler.png');
+saveas(a, 'euler2.png');
 
 %Part c.
 b = figure(2);
 y_heun = heun_sol_order1(@(t,y) ode2(t,y), dt, 1, [0 3]);
 plot(t, y_analytical(t), 'k-', t, y_heun, 'o-');
 title('Analytical vs. Heun')
 legend('Analytical', 'Heun', 'Location', 'Northeast')
-saveas(b, 'heun.png');
+saveas(b, 'heun2.png');

HW6Problem3.m

@@ -1,23 +1,30 @@
-%Part b.
-dy = ode3(0, [1;0]);
-dt = [0.1 0.01 0.001];
-figure()
-hold on
-for k = 1:length(dt)
-    t = [0:dt(k):3]';
-    y_n = zeros(length(t), 2);
-    y_n(1, :) = [1 0]; %initial condition
-    for i = 2:length(t)
-        dy = ode3(t, y_n(i-1, :));
-        y_n(i, :) = y_n(i-1, :) + dt(k)*dy;
-    end
+%Part a.
+y_analytical = @(t) cos(3*t); 
 
-    plot(t, cos(3*t), 'k-', t, y_n(:,1), 'o-');
+%Part b.
+dt = 0.001; %step size
+a = figure(1);
+set(0, 'defaultAxesFontsize', 16)
+set(0, 'defaultTextFontsize', 16)
+set(0, 'defaultLineLineWidth', 2)
+t = [0:dt:3]';
+y_n = zeros(length(t), 2);
+y_n(1, :) = [1 0]; %initial condition
+for i = 2:length(t)
+    dy = ode3(t, y_n(i-1, :));
+	y_n(i, :) = y_n(i-1, :) + dt(k)*dy;
 end
+plot(t, y_analytical(t), 'k-', t, y_n(:,1), 'o-');
+title('Analytical vs. Euler')
+legend('Analytical', 'Euler', 'Location', 'Northeast')
+saveas(a, 'euler3.png');
 
 %Part c.
-figure()
+b = figure(2);
 dt = 0.001;
 t = [0:dt:3];
 y_heun = heun_sol_order2(@(t,y) ode3(t,y), dt, [1 0], [0 3]);
-plot(t, cos(3*t), 'k-', t, y_heun(:,1), 'o-');
+plot(t, y_analytical(t), 'k-', t, y_heun(:,1), 'o-');
+title('Analytical vs. Heun')
+legend('Analytical', 'Heun', 'Location', 'Northeast')
+saveas(b, 'heun3.png');

HW6Problem3.m~

@@ -0,0 +1,26 @@
+%Part a.
+y_analytical = @(t) cos(3*t); 
+
+%Part b.
+dt = 0.01; %step size
+a = figure(1);
+set(0, 'defaultAxesFontsize', 16)
+set(0, 'defaultTextFontsize', 16)
+set(0, 'defaultLineLineWidth', 2)
+t = [0:dt:3]';
+y_n = zeros(length(t), 2);
+y_n(1, :) = [1 0]; %initial condition
+for i = 2:length(t)
+    dy = ode3(t, y_n(i-1, :));
+	y_n(i, :) = y_n(i-1, :) + dt(k)*dy;
+end
+
+    plot(t, cos(3*t), 'k-', t, y_n(:,1), 'o-');
+end
+
+%Part c.
+figure()
+dt = 0.001;
+t = [0:dt:3];
+y_heun = heun_sol_order2(@(t,y) ode3(t,y), dt, [1 0], [0 3]);
+plot(t, cos(3*t), 'k-', t, y_heun(:,1), 'o-');

README.md

@@ -13,7 +13,6 @@ a = figure(1);
 set(0, 'defaultAxesFontsize', 16)
 set(0, 'defaultTextFontsize', 16)
 set(0, 'defaultLineLineWidth', 2)
-hold on
 t = [0:dt:3]';
 y_n = zeros(size(t));
 y_n(1) = 1; %initial condition
@@ -35,5 +34,52 @@ legend('Analytical', 'Heun', 'Location', 'Northeast')
 saveas(b, 'heun.png');
 ```
 
-### Part a.
-![Analytical vs. Euler](./euler.png)
+### Part b.
+![Analytical vs. Euler](./euler2.png)
+
+### Part c.
+![Analytical vs. Heun](./heun2.png)
+
+## Problem 3
+
+### Script:
+```matlab
+%Part a.
+y_analytical = @(t) cos(3*t); 
+
+%Part b.
+dt = 0.001; %step size
+a = figure(1);
+set(0, 'defaultAxesFontsize', 16)
+set(0, 'defaultTextFontsize', 16)
+set(0, 'defaultLineLineWidth', 2)
+t = [0:dt:3]';
+y_n = zeros(length(t), 2);
+y_n(1, :) = [1 0]; %initial condition
+for i = 2:length(t)
+    dy = ode3(t, y_n(i-1, :));
+	y_n(i, :) = y_n(i-1, :) + dt(k)*dy;
+end
+plot(t, y_analytical(t), 'k-', t, y_n(:,1), 'o-');
+title('Analytical vs. Euler')
+legend('Analytical', 'Euler', 'Location', 'Northeast')
+saveas(a, 'euler3.png');
+
+%Part c.
+b = figure(2);
+dt = 0.001;
+t = [0:dt:3];
+y_heun = heun_sol_order2(@(t,y) ode3(t,y), dt, [1 0], [0 3]);
+plot(t, y_analytical(t), 'k-', t, y_heun(:,1), 'o-');
+title('Analytical vs. Heun')
+legend('Analytical', 'Heun', 'Location', 'Northeast')
+saveas(b, 'heun3.png');
+```
+
+### Part b.
+![Analytical vs. Euler](./euler3.png)
+
+### Part c.
+![Analytical vs. Heun](./heun3.png)
+
+## Problem 4