Given three unequally spaced points (xi,yi), (xi+1,yi+1) , and (xi+2,yi+2), use Taylor series ex

Name: Given three unequally spaced points (xi,yi), (xi+1,yi+1) , and (xi+2,yi+2), use Taylor series expansion to develop a finite difference formula to evaluate the first derivative dy/dx at the point x = xi . Verify that when the spacing between these points is equal, the three-point forward difference formula is obtained. The answer should involve yi, yi+1, and yi+2.
Uploaded: 2023-07-17T12:15:05-08:00
Duration: 2 min 44 s
Channel: Adi S
Description: Given three unequally spaced points (xi,yi), (xi+1,yi+1) , and (xi+2,yi+2), use Taylor series expansion to develop a finite difference formula to evaluate the first derivative dy/dx at the point x = xi . Verify that when the spacing between these points is equal, the three-point forward difference formula is obtained. The answer should involve yi, yi+1, and yi+2.

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Adi S · Accepted Answer

To begin, we need to find the Taylor series expansion for dy/dx at X. We can do this by substitu

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