Finite difference approximation question

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SUMMARY

The discussion centers on the finite difference approximation formula for the derivative u'(xj-1/2) and its relationship with the parameter θ. The approximation is expressed as u'(xj-1/2) + λu(xj−1/2) ≈ 1/h*[u(xj ) − u(xj−1)] + λ(θu(xj ) + (1 − θ)u(xj−1)). The main inquiry is to determine the order of approximation as a function of θ, highlighting the need for clarity in finite difference methods. The lack of responses indicates a gap in knowledge sharing regarding this specific mathematical topic.

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volcano90
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Hi,

I have a question regarding finite difference approximation:
Consider the finite difference approximation
u'(xj-1/2) + λu(xj−1/2) ≈ 1/h*[u(xj ) − u(xj−1)] + λ(θu(xj ) + (1 − θ)u(xj−1))

how can I Find the order of approximation as a function of θ?

I am really new in this field, so appreciate any kind answer.

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