How can i solve this problem with matrices ?

How can i solve this problem:

[A]{x}+[B]{x'}+[C]{x''}={K}

A,B,C:known matrices K:known vector (nx1)

and x'' derivative of x' and x' derivative of x(unknown)

[Sara]

rewrite the equation as a system of two first order ODE's. then use ode45 or ode15s.

[Charis Theodorou]

Can u give me an example??

[Sara]

Set x' = y so that x" = y', then:

A * x + B * y + C * y'= K
x' = y

rewrite as

y' = ...
x' = ...

then from the main code, use ode45 (non-stiff) or ode15s (stiff). Look also here: http://www.mathworks.com/matlabcentral/answers/66301-solve-a-second-order-differential-equation

[Charis Theodorou]

Thanks a lot!! I hope that this is the solution!! If not i will be back.

[Roger Stafford]

I think this is what Sara means: Assuming matrix C is n-by-n and invertible, multiply both sides of your equation by inv(C) to get:

 x'' = -(C\B)*x'-(C\A)*x+(C\K)

Now write

 x' = y;
 y' = -(C\B)*y-(C\A)*x+(C\K)

Your equations are now in standard form for any of the 'ode' solvers. You have 2*n equations to evaluate in each call to your required ode function.

[Sara]

Yes, that's a more rigorous way to put it. I gave the condition on C for granted.

[Charis Theodorou]

Thanks again!!

[Charis Theodorou]

if C has zeros in the last row and column how can i solve it??

[Charis Theodorou]

Also can you remind me how i write the ode45 when i have a vector(nx1) and not a number?

[Charis Theodorou]

 I call this function with ode(@diplomatiki, [0 20], zeros(n+3,2))

It might be an error regarding dimensions since I am not sure how to cope with vectors

[Charis Theodorou]

Can you help me with this problem???

[Sara]

Can you post the entire code, including A, B and C?

[Charis Theodorou]

This is the code !!

[Charis Theodorou]

the equation is: [Mol]{x''}+[Col]{x'}+[Kol]{x}=Z

[Charis Theodorou]

can be solved ??