hw09_p04_answer - Problem 4. Nonlinear BVP with a shooting...

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Problem 4. Nonlinear BVP with a shooting method combined with RK4 or the trapezoidal rule predictor corrector Are they nearly the same? Yes! The two results in (a) and (b) are similar each other. But we were able to confirm that the resuts from RK4 were closer to the real solutions than those of trapezoidal rule predictor-corrector in previous HWs. (a) With trapezoidal predictor-corrector method h = 0.20000 Tolerance = 0.0001000 y( 0.00000)= 0.00000, y( 2.00000)= 3.00000 1 st guess = 0.00000, 2 nd guess = 0.50000 x Y1(x) iter 1 2 3 4 5 6 7 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.20000 0.02000 0.12000 0.06208 0.07272 0.07719 0.07684 0.07685 0.40000 0.07240 0.27665 0.15829 0.18004 0.18917 0.18845 0.18847 0.60000 0.15146 0.46957 0.28497 0.31883 0.33305 0.33194 0.33196 0.80000 0.25275 0.70188 0.44043 0.48821 0.50830 0.50672 0.50676 1.00000 0.37325 0.98209 0.62557 0.69026 0.71751 0.71538 0.71543 1.20000 0.51157 1.32781 0.84492 0.93142 0.96800 0.96513 0.96520 1.40000
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hw09_p04_answer - Problem 4. Nonlinear BVP with a shooting...

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