# How to convert PDE into matrix form

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Sandeep Nair on 25 Nov 2022
Edited: Torsten on 28 Nov 2022
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
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Sandeep Nair on 25 Nov 2022
Please find the form in which i want,i have attached the fig

Torsten on 25 Nov 2022
Edited: Torsten on 25 Nov 2022
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).
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Torsten on 28 Nov 2022
Edited: Torsten on 28 Nov 2022
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]