Question

Here is 11.1 for reference. I need help with 11.3

11.3 Concepts: Error Order and Precision pts The following is a 5-point backward difference scheme, over equally-spaced x, for df/dx at xx 25/,-48f-+36f-2-16-3+34 12 Ar Write out Taylor Series expressions for each of the four fa, f f fto the SIXTH derivative, like you did in 11.1, and then combine them using the difference scheme above to a) Calculate the discretization error order (i.e. write the erro(Ax) for some integer p) b) Calculate the precision of the scheme. Hint: DON'T write a Taylor Series for f. f, is just itself (or just written as f(x)). There's nothing else you can do with it. Only ever create Taylor Series expansions for points other than f 11.1 Application: Finite Difference Rules 2 pts This is the equation for the Taylor Series expansion of f(x+), as a function of fx) and all its derivatives at x, that will be given to you on your midterm and exam cheat-sheets: x + 3! 4! Start with that equation and use it to derive the expression for f(x,-3Ax) (i.e.fx) evaluated three nodes to the left of x) as a function of fx) and all the derivatives at x, up to the SIXTH derivative

Answer 1

TN 3

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