From f71e05449df9e021ef8ae1c9f0691e988392e691 Mon Sep 17 00:00:00 2001 From: Matthew Balnis Date: Tue, 5 Dec 2017 16:10:52 -0500 Subject: [PATCH] Updated readme --- HW6Problem4.m | 45 ++++++++++++++++++++++++++------------------- README.md | 48 +++++++++++++++++++++++++++++++++++++++++++++++- euler4.png | Bin 0 -> 38478 bytes heun3.png | Bin 34445 -> 38414 bytes heun4.png | Bin 0 -> 38414 bytes 5 files changed, 73 insertions(+), 20 deletions(-) create mode 100644 euler4.png create mode 100644 heun4.png diff --git a/HW6Problem4.m b/HW6Problem4.m index fd9e0c7..e7712a9 100644 --- a/HW6Problem4.m +++ b/HW6Problem4.m @@ -1,27 +1,34 @@ %part a. -t = [0:.1:12]; g = 9.81; %m/s^2 cd = 0.25; %kg/m m = 60; %kg v_term = sqrt(m*g/cd); x_analytical = @(t) ((v_term^2)/g)*log(abs(cosh((g*t)/v_term))) + 100; - -plot(t, x_analytical(t)) - %part b. -%dy = ode4(0, [1;0]); -dt = [0.1 0.01]; -figure() -hold on -for k = 1:length(dt) - t = [0:dt(k):12]'; - y_n = zeros(length(t), 2); - y_n(1, :) = [100 0]; %initial condition - for i = 2:length(t) - dy = ode4(t(i-1), y_n(i-1, :)); - y_n(i, :) = y_n(i-1, :) + dt(k)*dy; - end - %[t23, y23] = ode23(@(t,y) phugoid_ode(t,y), [0,20], [10 0 0 2]); - plot(t, x_analytical(t), '.', t, y_n(:,1), 's'); -end \ No newline at end of file +dt = 0.01; %step size +a = figure(1); +set(0, 'defaultAxesFontsize', 16) +set(0, 'defaultTextFontsize', 16) +set(0, 'defaultLineLineWidth', 2) +t = [0:dt:12]'; +y_n = zeros(length(t), 2); +y_n(1, :) = [100 0]; %initial condition +for i = 2:length(t) + dy = ode4(t, y_n(i-1, :)); + y_n(i, :) = y_n(i-1, :) + dt(k)*dy; +end +plot(t, x_analytical(t), 'k-', t, y_n(:,1), 'o-'); +title('Analytical vs. Euler') +legend('Analytical', 'Euler', 'Location', 'Northeast') +saveas(a, 'euler4.png'); + +%Part c. +b = figure(2); +dt = 0.01; +t = [0:dt:12]; +y_heun = heun_sol_order2(@(t,y) ode4(t,y), dt, [100 0], [0 12]); +plot(t, x_analytical(t), 'k-', t, y_heun(:,1), 'o-'); +title('Analytical vs. Heun') +legend('Analytical', 'Heun', 'Location', 'Northeast') +saveas(b, 'heun4.png'); \ No newline at end of file diff --git a/README.md b/README.md index 4dc6d88..168ac11 100644 --- a/README.md +++ b/README.md @@ -82,4 +82,50 @@ saveas(b, 'heun3.png'); ### Part c. ![Analytical vs. Heun](./heun3.png) -## Problem 4 \ No newline at end of file +## Problem 4 + +### Script: +```matlab +%part a. +g = 9.81; %m/s^2 +cd = 0.25; %kg/m +m = 60; %kg +v_term = sqrt(m*g/cd); +x_analytical = @(t) ((v_term^2)/g)*log(abs(cosh((g*t)/v_term))) + 100; + +%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:12]'; +y_n = zeros(length(t), 2); +y_n(1, :) = [100 0]; %initial condition +for i = 2:length(t) + dy = ode4(t, y_n(i-1, :)); + y_n(i, :) = y_n(i-1, :) + dt(k)*dy; +end +plot(t, x_analytical(t), 'k-', t, y_n(:,1), 'o-'); +title('Analytical vs. Euler') +legend('Analytical', 'Euler', 'Location', 'Northeast') +saveas(a, 'euler4.png'); + +%Part c. +b = figure(2); +dt = 0.01; +t = [0:dt:12]; +y_heun = heun_sol_order2(@(t,y) ode4(t,y), dt, [100 0], [0 12]); +plot(t, x_analytical(t), 'k-', t, y_heun(:,1), 'o-'); +title('Analytical vs. Heun') +legend('Analytical', 'Heun', 'Location', 'Northeast') +saveas(b, 'heun4.png'); +``` + +### Part b. +![Analytical vs. Euler](./euler4.png) + +### Part c. +![Analytical vs. Heun](./heun4.png) + + diff --git a/euler4.png b/euler4.png new file mode 100644 index 0000000000000000000000000000000000000000..38b90cb94b21bbf2bdea4375ab7ae296f3b1bcff GIT binary patch literal 38478 zcmdSBXH-<%)-777TQQ(0Vn7j5LzKVUm`?Y)Dz3sjBem&Yg%{s7ZuDNCyqmSPET>dIb=NZB z+=1)&5!auwH@)a+X=l4v!_vl-#4mJM+Vs-lWBf;t?>#Ck!hc*uKv+UE4s8DC8Q)JaEt^4=CNMEv_g`v0&0=KUBUku>CFWo0E6{sd*eX=-x%_4)aa zfrmHptlI*kqWH>(x=P&#n<;6P#e?RR*98hEe%7*`w0~2Ow>0x!LR3slu_=f=nYGe; zbGin1Na0@+DWo=-OI<6&AcZ%JN>x-+vi%%$qp;{Qy`A0Y%*?gfz7``dG0*uK^7zP{ zu6?(HZGU}2Lz43G44ccBdwDWTOj4sX(jKys?o}wrkPcDbKV!b2s 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