MATLAB: Solving system of ODE using ode45 in matlab

Question

an example of using 2 to 4 ode's

Answer 1

clc

clear

n = 30;

t = [0 0.52 1.04 1.75 2.37 3.25 3.83]';

x = [153 185 208 249 261 271 273]';

tt = linspace(t(1),t(end),n);

xx = spline(t,x,tt);

v = calc_derv(tt,xx);

a = calc_derv(tt,v);

subplot(2,1,1),plot(tt,v)

title('Jet Fighters Velocity')

xlabel('Time (s)')

ylabel('Velocity (m/s)')

subplot(2,1,2),plot(tt,a)

title('Jet Fighters Acceleration')

xlabel('Time (s)')

ylabel('Acceleration (m/s^2)')

% calculate 1st order derivative using finite differences

function dydx = calc_derv(x,y);

n = length(x);

h = x(2)-x(1);

dydx(1) = (-y(3) + 4*y(2) - 3*y(1))/(2*h);

dydx(n) = (3*y(n) - 4*y(n-1) + y(n-2))/(2*h);

for i = 2:n-1

dydx(i) = (y(i+1) - y(i-1))/(2*h);

end