- C Calculate The Leading Order Error For The L Rule On A Subinterval Of Width Ar D In View Of Your Answer To Par 1 (26.16 KiB) Viewed 47 times
The L_4 quadrature rule for [-1,1] uses four nodes: t_1 = -1 t_4 = 1 and t_2 and t_3 are chosen optimally to minimise the error.
(c) Calculate the leading order error for the L, rule on a subinterval of width Ar. (d) () In view of your answer to part (c). make a fair comparison of the La quadrature rule and the three-point Gaussian rule. (ii) Suppose that after performing a calculation with the La rule on N subintervals, a second calculation us made, this time using 2N subintervals. How many new evaluations of the integrand are required? What is the corresponding value for the three-point Gaussian rule (i.e. how many new evaluations are required to apply the rule on 2N subintervals if it has already been applied on N subintervals)? Explain your answers.