Let fj= f(x), where r, are equispaced points with constant grid spacing h. A finite- difference...

 

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Let fj= f(x), where r, are equispaced points with constant grid spacing h. A finite- difference approximation of the first derivative is -2f₁-1-3f; +6fj+1 - fj+2 6h f'(x₂) Use Taylor's (Lagrange Remainder) theorem to show that the error of the first-derivative approximation (1) is O(h³). (1) Let fj= f(x), where r, are equispaced points with constant grid spacing h. A finite- difference approximation of the first derivative is -2f₁-1-3f; +6fj+1 - fj+2 6h f'(x₂) Use Taylor's (Lagrange Remainder) theorem to show that the error of the first-derivative approximation (1) is O(h³). (1)

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Solution To solve it we need to use Taylors theorem which gives an approximation of a function by a polynomial of a certain degree Taylors theorem say... View the full answer