Numerical Method Based on Taylor series, we need to numerically estimate the 1\"
ID: 1861377 • Letter: N
Question
Numerical Method
Based on Taylor series, we need to numerically estimate the 1" derivative fx) where the locally continuous function. f(x) is shown in the following figure. (Forward Finite Difference Method) Suppose that we have evaluated the function f(x) at x= xi, and x= xi+1 as f(xi,) and f(xi+1]) respectively. Let h= xi+1- xi. Derive the formula to estimate f(xi) step-by-step. (Backward Finite Difference Method) Suppose that we have evaluated the function f(x) at x= xi, and x= xi-1 and f(xi-1) respectively Let h= xi-xi-1. Derive the formula to estimate f(xi) step-by-step.Explanation / Answer
Forward finite
[f(x i+1) -f(x i)]/(xi+1 - xi) = f'(xi) equating slope with f'(xi) where i>=0
backward difference
[f(x i) -f(x i-1)]/(xi - xi-1) = f'(xi) equating slop with f'(xi) where i>=1
hence derived, but hust equating actual slope with f'(xi)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.