How can I solve this Ode system?

Hello guys. So I have this parabolic PDE which I convert it to an ODE system via Finite element method on a small domain say :

Y=[0 0.06250]x[0 0.06250]

the system is:

D m' = K m + F

m(0)=0

which K is the stiffness matrix (81x81) and F is the load matrix (81x1)and D is a (81x1) matrix. the result should be a (81x1) matrix for m. Can you please tell me how to solve this system in Matlab at a time node for example 1?

thanks in advance

Answer 1

[Yu Jiang]

I can run your code with

[T,Y] = anzyme1(eye(81),eye(81), ones(81,1), 10)

What are the parameters you use such that you see the error message?

[Navid]

It seems there was something wrong with my "D" matrix. Thanks.

Answer 2

[Yu Jiang]

Navid

You can find quite a few details and examples in the documentation.

http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html

-Yu Jiang

[Navid]

Thanks Yu,

I know about that but something is wrong about my code which I can't figure it out.Here is my code:

function [T,Y]=anzyme1(D,K,F,Delta)

%this is a function to solve the ode system: D m' = K m + F

this function takes D which is a constant (81x81) matrix I calculated

from the FEM stage. K is stiffness matrix again constant and (81x81)

and my loda vector being F which is a constant (81x1) matrix

Delta : the final time which I need to have the solution in.

f1=@(t,m) (K*m)+F;       

       %here I defined a function which describes the RHS  

options=odeset('Mass',D); 

        %the Mass matrix is D which is a matrix with constant entries

m0=zeros([81 1]);        

         %my initial value is zero everywhere.

[T,Y]=ode23s(f1,[0,Delta],m0,options);  

         %I used ode23s to solve my ode system

and when I run it it says:

Warning: Failure at t=1.872630e-006.  Unable to meet integration tolerances without
reducing the step size below the smallest value allowed (6.652917e-021) at time t.

Please help me.