Question

23.8 The following nonlinear, parasitic ODE was suggested by Hornbeck (1975): d y di 5 ) If the initial condition is y(0) -0.08, obtain a solution from t-0 to 5: (a) Analytically (b) Using the fourth-order RK method with a constant step size of 0.03125. (c) Using the MATLAB function ode45. (d) Using the MATLAB function ode23s (e) Using the MATLAB function ode23tb. Present your results in graphical form.

I want Matlab code.

Answer 1

% lets use clc to clear command window
% clear all to delete previous data
% close all to close all privious figures
clc;
clear all;
close all;

tspan = [0 5];
y0 = 0.08;

%% with ODE45

[t1,y1] = ode45(@(t,y) 5*(y-(t*t)), tspan, y0);
plot(t1,y1)
title('ODE45')
%% with ODE23s

[t2,y2] = ode23s(@(t,y) 5*(y-(t*t)), tspan, y0);
figure
plot(t2,y2)
title('ODE23s')
%% with ODE23tb

[t3,y3] = ode23tb(@(t,y) 5*(y-(t*t)), tspan, y0);
figure
plot(t3,y3)
title('ODE23tb')

x 10 3 ODE45 2.5 2 1.5 0.5 0 0 0.5 1.5 22.5 3 3.5 4 4.5 5

x107 3 ODE23s 2.5 2 1.5 0.5 0 0 0.5 1.5 22.5 3 3.5 4 4.5 5

ODE23tb 20 15 10 -5 -10 -15 0 0.5 1.52 2.5 3 3.5 4 4.55