matlab function
function xdot = msd(t,x)% Function file for mass with spring and damping.
% Position is first variable, velocity is second variable.
u = 10;m = 1;c = 2;k = 5;A = [0, 1;-k/m, -c/m];B = [0; 1/m];xdot = A*x+B*u;[t, x] = ode45(@msd, [0,5], [0,0];
, which can be converted to two first order ODEs
theta_ic = [0.5; 0]; % initial conditions: theta(t=0)=0.5; dtheta(t=0)=0.
tspan = [0 10];[t, theta] = ode45(@odeFun, tspan, theta_ic);plot(t, theta);legend({'$\theta$', '$\dot{\theta}$'}, ... 'Location', 'best', ... 'Interpreter', 'latex', ... 'FontSize', 16)function dtheta = odeFun(t, theta) g = 9.8; l = 1; % theta(1) = theta, theta(2) = dtheta
dtheta = zeros(2, 1); dtheta(1) = theta(2); dtheta(2) = -g/l*theta(1);end
%define parameters
%x is the number of cancer cells
x0 = 1000;% c2 is the number of bad stromal cells
c2 = 30;%b is the number of bad stroma cells (ratio)
b = 20; % a is the growth rate of cancer cells
a = 0.35;% a2 growth rate of cancerous stroma
a2 = 0.4;%time parameter (measured in weeks)
t0=0; %initital time
t1=520; %final time
tspan=[t0 t1];% plot result
[t, x] = ode45(@(t,x)badstromarun(t,x,a2,a,b,c2),tspan,x0); figure(1)plot(t,x)% function
function xdot= badstromarun(~,x,a2,a,b,c2)xdot = zeros(1,1);xdot(1) = (a.*x).*(1-log(x)/b)*(c2/(a2+c2));end
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