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I am new to this community but by reviwwing the questions and answers posted in this forum I was encouraged to share my question with you and I hope you can help me.

I have a system of 4th order ordinary differential equations for several functions which I call them:

[tex]y_1,y_2, ..., y_n[/tex] and all of them are single variable functions e.g. [tex]y_1 = f(x)[/tex]

The system looks like:

[tex]\left\{y_1', y_1'', y_1''', y_1^{(4)}, y_2', y_2'', y_2''', y_2^{(4)}, ... y_n', y_n'', y_n''', y_n^{(4)}\right\}^{T}=\left[A\right] \left\{y_1, y_1', y_1'', y_1''', y_2, y_2', y_2'', y_2''', ... y_n, y_n', y_n'', y_n'''\right\}^{T}[/tex]

Where [tex]\left[A\right][/tex] is the coefficient matrix.

In short form this equation can be written as:

[tex]\left\{Y'\right\} = \left[A\right] \left\{Y\right\}[/tex]

Now, my question is that if the eigenvalue method is accurate enough to solve this system of equation or I should use a different method to solve such system of ODEs.

I am waiting for your valuable comments.