Given the non-uniform grid as follows: A1 Uj-1 uj Uj+1 Figure 1: Non-uniform grid. The spacing...

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Given the non-uniform grid as follows: A1 Uj-1 uj Uj+1 Figure 1: Non-uniform grid. The spacing between u;_1 and u; is Ax, and between Ax1 Ax2 and Uj+1 is Ax2, 1. Derive a 3-point central differencing scheme for the second derivative using the solution values at j- 1, j, j + 1 . 2. What is the error term and the order of accuracy for the above scheme? Given the non-uniform grid as follows: A1 Uj-1 uj Uj+1 Figure 1: Non-uniform grid. The spacing between u;_1 and u; is Ax, and between Ax1 Ax2 and Uj+1 is Ax2, 1. Derive a 3-point central differencing scheme for the second derivative using the solution values at j- 1, j, j + 1 . 2. What is the error term and the order of accuracy for the above scheme?

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1 To derive a 3point central differencing scheme for the second derivative we can use Taylor series ... View the full answer