How do I solve coupled ordinary differential equations with boundary conditions?

I have four coupled ODE's. I am not sure how to plot and solve them using Matlab. The equations are: dy(1)=y(2); dy(2)=10*((50000*y(1)*exp(-10/y(3)))+y(2)); dy(3)=y(4); dy(4)=10*((-100000*y(1)*exp(-10/y(3)))+y(4)); with following boundary conditions: y1(0) = 1, y3(0) = 0, y2(2) = 0, y4(2) = 0 I think they can be solved numerically, but I'm not sure how. can anyone help me with my problem? tnx

Answer 1

[Torsten]

function mat4bvp

solinit = bvpinit(linspace(0,2,10),[1 0 1e-5 0]);
sol = bvp4c(@mat4ode,@mat4bc,solinit);

x = linspace(0,2);
y = deval(sol,x);
plot(x,y(1,:),x,y(2,:),x,y(3,:),x,y(4,:))

% ------------------------------------------------------------
function dydx = mat4ode(x,y)
dydx = [  y(2)
         10*(50000*y(1)*exp(-10/y(3))+y(2))
          y(4)
         10*(-100000*y(1)*exp(-10/y(3))+y(4)) ];
% ------------------------------------------------------------
function res = mat4bc(ya,yb)
res = [  ya(1)-1 
         yb(2)
         ya(3) 
         yb(4) ];
% ------------------------------------------------------------

Best wishes

Torsten.

[kyana shayan]

thank you for your time Torsten, but I don't get it. should I open 3 scripts, and put the functions in each? can you tell me how this code works?