Question: 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

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

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

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