1. (20 pts.) Consider three values of a function T(): Tj, Tj+1, Tj+2 at mesh points...

 

Transcribed Image Text:

1. (20 pts.) Consider three values of a function T(): Tj, Tj+1, Tj+2 at mesh points 1;, Ij+1, 1+2 on a uniform mesh with spacing Az. Use the method of undetermined coefficients to find a finite difference approximation to the first derivative with respect to x at the mesh point j. 2. (20 pts.) The RMS error for a scheme has been found for different time steps and is tabulated below. Estimate the temporal order of the scheme. (Note: This was presented at the end of the Algorithm Analysis section of the Lecture Notes.) At RMS 0.125 0.012 0.25 0.051 0.5 0.19 1.0 0.75 1. (20 pts.) Consider three values of a function T(): Tj, Tj+1, Tj+2 at mesh points 1;, Ij+1, 1+2 on a uniform mesh with spacing Az. Use the method of undetermined coefficients to find a finite difference approximation to the first derivative with respect to x at the mesh point j. 2. (20 pts.) The RMS error for a scheme has been found for different time steps and is tabulated below. Estimate the temporal order of the scheme. (Note: This was presented at the end of the Algorithm Analysis section of the Lecture Notes.) At RMS 0.125 0.012 0.25 0.051 0.5 0.19 1.0 0.75

Answer rating: 100% (QA)

Question Step 1 Consider the function Recall the below formulae Forward difference formula of O h 2 ... View the full answer