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1)State the expression for the central difference representation of O(2) for nth derivative of a function. Derive the finite difference expression for the followings: i) (forward difference O(h)) ii) d (backward difference O(h)) df dx dx7 i) (central difference O(/) ii) iii) (central difference O(1²) dx³ dx

1)State the expression for the central difference representation of O(2) for nth derivative of a function. Derive the finite difference expression for the followings: i) (forward difference O(h)) ii) d (backward difference O(h)) df dx dx7 i) (central difference O(/) ii) iii) (central difference O(1²) dx³ dx

Advanced Engineering Mathematics
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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1)State the expression for the central difference representation of O(²) for nth derivative of a function. Derive the finite difference expression for the followings: df dx (forward difference O(h²)) ii). (backward difference O(h)) d' f dx7 iii) (central difference O(h) iii) d (central difference O(h²) dx dx iv) Using Richardson's extrapolation method, obtain the finite difference representation of O(h) for first and second derivatives of a function.
Transcribed Image Text:1)State the expression for the central difference representation of O(²) for nth derivative of a function. Derive the finite difference expression for the followings: df dx (forward difference O(h²)) ii). (backward difference O(h)) d' f dx7 iii) (central difference O(h) iii) d (central difference O(h²) dx dx iv) Using Richardson's extrapolation method, obtain the finite difference representation of O(h) for first and second derivatives of a function.
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