How to convert PDE into matrix form

i have a partial differential equation like

m1*diff(x1(t), t, t) + c1*x1d + k1*x1 + (c2*(2*x1d - 2*x2d))/2 + (k2*(2*x1 - 2*x2))/2 =0

m2*diff(x2(t), t, t) - (c2*(2*x1d - 2*x2d))/2 - (k2*(2*x1 - 2*x2))/2 = 0

and i want to bring this form into

matrix form of x1 ,how is it possible to do in matlab

[Torsten]

This is not a partial differential equation, but two second-order ordinary differential equation for functions x1 and x2.

What do you mean by "matrix form of x1" ?

[Sandeep Nair]

Please find the form in which i want,i have attached the fig

Answer 1

[Torsten]

Can you write this in matrix form ?

m1*diff(x1(t), t, t) + 0*m2*diff(x2(t), t, t)  + (c1 + c2) * x1d - c2 * x2d + (k1 + k2) * x1 - k2 * x2 = 0
0*diff(x1(t), t, t)  + m2*m2*diff(x2(t), t, t) - c2        * x1d + c2 * x2d - k2        * x1 + k2 * x2 = 0

This is something you must do by yourself. MATLAB can't help you with this (or only with a lot of effort in advance from your side).

[Sandeep Nair]

Hi,am not able to write in this form hence wanted help from this forum on how to do it

[Torsten]

But exactly this system is already written in matrix form in your attached "Matrixformulation.png" with P1(t) and P2(t) being 0. So what exactly is your question ?

I already wrote that MATLAB has no tool to convert written equations in matrix form - that's a task you have to do by yourself.

E.g. if you have the 2 equations

a1*x + b1*y = c1
a2*x + b2*y = c2

you can write them in matrix form as

U*z = w

with

U = [a1 b1 ; a2 b2], z = [x;y], w = [c1;c2]