Question: 4. Consider Table 8.13 in the textbook. Using the approximations at x = 10.0 with h = 0.125 and h= 0.25, estimate the order of

4. Consider Table 8.13 in the textbook. Using the approximations at x = 10.0 with h = 0.125 and h= 0.25, estimate the

4. Consider Table 8.13 in the textbook. Using the approximations at x = 10.0 with h = 0.125 and h= 0.25, estimate the order of convergence of the method. Apply Richardson extrapolation to obtain a more accurate approximation of the solution at r = 10.0. Apply Richardson error estimate to estimate the error at r= 10.0 with h = 0.125. Table 8.13. Example of Fourth-Order Fehlberg Formula (8.86) 0.25 2.0 4.0 6.0 8.0 10.0 2.0 4.0 ys(x) 0.493136301 -1.410449823 0.680752304 0.843864007 -1.383094975 0.493150889 -1.410446334 0.680754675 0.843858525 -1.383092786 YO) - (x) -5.71E-6 3.71E-6 2.48E-6 -5.79E-6 2.34E-6 -2.99E-7 2.17E-7 1.14E-7 --3.12E-7 1.46E-7 (x) - (x) -9.49E-7 1.62E-6 -3.97E-7 -1.29E-6 1.47E-6 -235E-8 4.94E-8 -1.76E-8 -3.47E- 4.65E-8 8.0 10.0 4. Consider Table 8.13 in the textbook. Using the approximations at x = 10.0 with h = 0.125 and h= 0.25, estimate the order of convergence of the method. Apply Richardson extrapolation to obtain a more accurate approximation of the solution at r = 10.0. Apply Richardson error estimate to estimate the error at r= 10.0 with h = 0.125. Table 8.13. Example of Fourth-Order Fehlberg Formula (8.86) 0.25 2.0 4.0 6.0 8.0 10.0 2.0 4.0 ys(x) 0.493136301 -1.410449823 0.680752304 0.843864007 -1.383094975 0.493150889 -1.410446334 0.680754675 0.843858525 -1.383092786 YO) - (x) -5.71E-6 3.71E-6 2.48E-6 -5.79E-6 2.34E-6 -2.99E-7 2.17E-7 1.14E-7 --3.12E-7 1.46E-7 (x) - (x) -9.49E-7 1.62E-6 -3.97E-7 -1.29E-6 1.47E-6 -235E-8 4.94E-8 -1.76E-8 -3.47E- 4.65E-8 8.0 10.0

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