csci 317 numerical analysis

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You should type them. The latter caries 2 real points extra.

Problem 1.

Given the function , where are data points. Find the system of linear equations you may use to calculate

Note: Denote the , for j=1,2,…., for the mixed sums use the notations as those shown in class.

Problem 2

a) Find the approximation of the function derivatives . Use the forward difference formula for the 1^st derivative, backward for the 2^nd, and central formula for the 3^rd derivative. Apply the formalism: ; and which leads to .

b) Write the truncation error of the forward with respect to , backward and the central 1^st order derivatives with respect to of the function ?

c) What is the truncation error of the second derivative central formula approximation of g(x)?