12.3 7 pts 8'(x)=(-123+ Finite Difference Rules: Error Order and Precision Here's a 5-point central scheme for d2f/dx? - fi-2 +16f;-1 30f; +16f;+1 - Fit2 + Error at x = xi, assuming equally-spaced x: 12 Ar2 a) Write out Taylor Series expressions for each of the four fi-z, fi-1, fi+1, fit2 to the SIXTH derivative. b) Substitute all four Taylor Series expressions into the right-hand side of the difference scheme above to determine the remaining Error term(s), and from that determine ... the discretization error order (i.e. write Error = O(AxP) for some integer p), the precision of the scheme. Hint: DON'T write a Taylor Series for fi. f; is just itself (or just written as f(xi)). There's nothing else you can do with it. Only ever create Taylor Series expansions for points other than fi. 12.3 7 pts 8'(x)=(-123+ Finite Difference Rules: Error Order and Precision Here's a 5-point central scheme for d2f/dx? - fi-2 +16f;-1 30f; +16f;+1 - Fit2 + Error at x = xi, assuming equally-spaced x: 12 Ar2 a) Write out Taylor Series expressions for each of the four fi-z, fi-1, fi+1, fit2 to the SIXTH derivative. b) Substitute all four Taylor Series expressions into the right-hand side of the difference scheme above to determine the remaining Error term(s), and from that determine ... the discretization error order (i.e. write Error = O(AxP) for some integer p), the precision of the scheme. Hint: DON'T write a Taylor Series for fi. f; is just itself (or just written as f(xi)). There's nothing else you can do with it. Only ever create Taylor Series expansions for points other than fi