For example, when we solve simple 1D Poisson equation by finite difference method, why three point central difference scheme on uniform grid (attached image) is second order method for solution convergence?(adsbygoogle = window.adsbygoogle || []).push({});

I understand why approximation of first derivative is second order (and that second derivative is also second order because cancelation of first order truncation error term on uniform grid), but I don’t understand why solution also converges with second order.

Basically, this approximation is equivalent to fitting local quadratic (p=2) polynomial through three points which should theoretically yield third (p+1) order method?

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# A Convergence order of central finite difference scheme

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