(a) Derive a finite difference formula for the first derivative by using three terms plus the remainder of the Taylor series expansion for a set of points that is not equally spaced. The solution should the derivative at point x=xi in terms of X₁, X₁-1, X₁-2, X₁-3, f(xi), f(x-1), f(x-2) and f(xi- 3). (b) Derive a simplified formula in the case of equally spaced points. Submit your hand calculations.
(a) Derive a finite difference formula for the first derivative by using three terms plus the remainder of the Taylor series expansion for a set of points that is not equally spaced. The solution should the derivative at point x=xi in terms of X₁, X₁-1, X₁-2, X₁-3, f(xi), f(x-1), f(x-2) and f(xi- 3). (b) Derive a simplified formula in the case of equally spaced points. Submit your hand calculations.
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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