Answer is given BUT need full detailed steps andprocess since I don't understand the concept. **Using Taylor Series Expansions to Determine the Error in the Approximation**To approximate the fourth derivative of \( u \) at \( t \), we use the following expression:\[u^{iv}(t) \approx \frac{u(t+2h) - 4u(t+h) + 6u(t) - 4u(t-h) + u(t-2h)}{h^4}\]This simplifies to:\[= \frac{h^4 u^{iv} + \frac{1}{6} h^6 u^{(vi)}}{h^4}\]\[ = u^{iv} + \frac{1}{6} h^2 u^{(vi)}\]The last term, \(\frac{1}{6} h^2 u^{(vi)}\), represents the error in the approximation.**Hint**: Expand \( u(t + 2h) \), etc., using Taylor series up to the \( h^6 \) term.

Answered: Use Taylor series expansions to…

Math

Advanced Math

Use Taylor series expansions to determine the error in the approximation

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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