Hello, I'm trying to solve a differential equation with boundary conditions which leads me to an infinite system of linear equations.(adsbygoogle = window.adsbygoogle || []).push({});

I can obtain an approximate solution of the problem just by considering only the first n terms so I have a system of n equations with n unknowns.

I've been trying to find an exact solution of the problem by other methods but I always failed, and I suspect that the boundary conditions are incompatible so the exact solution does not exist and that's what I'm trying to prove now.

I noticed that the condition number of the system (computationally calculated of course) increases as n increases and that could be a prove that when n is infinite so is the condition number and therefore the matrix is singular.

However I don't know how to prove this mathematically, I only can calculate the variation of the contidion number with n for n from 5 to 300 or maybe 400, no more.

Does anyone have some ideas to help me???

Thank you so much in advance!!

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# How to know if an infinite system of linear equations has a solution

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