How to solve coupled differential equation in a limited range of the variable?

I need to solve the following set of coupled equations.(these are not the exact equations,but a similar example)

x'=y+x;

y'=2x+y+p;

where

p = y-7 if y>7

= 0 else

I dont know what type they fall into. I have tried using 'dsolve' but to no avail. Any specific matlab function for this case, or even a link to solving such equations would be greatly appreciated.

Thanks in advance.

[Karan Gill]

Did you try the numeric ode solvers?

Answer 1

[Star Strider]

This seems to work:

y = linspace(0,10);

p = (y-7).*(y>7);

figure(1)
plot(y, p)
grid

% % % MAPPING: x = z(1),  y = z(2)
de = @(t,z) [z(2) + z(1); 2*z(1) + z(2) + (z(2)-7).*(z(2)>7)];

ts = [0 10];

[T,Z] = ode15s(de, ts, [0.1; 0]);

figure(2)
semilogy(T, Z)
grid

Numerical ODE solvers tend not to do well with discontinuities. That does not seem to be a problem here, probably because ‘p’ is not a ‘step’ or other abrupt discontinuity.

[Chinmay Sharma]

Thanks.It works for the given problem.I wasnt aware of using '.*' for specifying bounds for numeric solvers.

[Star Strider]

My pleasure.

The ‘.*’ does not create bounds.

This syntax uses element-wise multiplication (the ‘.*’) to multiply ‘(z(2)-7)’ and a logical vector created by ‘(z(2)>7)’ in:

(z(2)-7).*(z(2)>7)

The logical vector is 0 for ‘z(2)<=7’ and 1 elsewhere. Logical vectors automatically convert from logical types to numerical (0,1) vectors in calculations.

[Chinmay Sharma]

Thanks again! Good to know.

[Star Strider]

My pleasure!