hw08_p03_answer - 0.43074 0.43077 -0.00003 2.00000 0.39999...

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Problem 3 The first four points have the same values as those from RK4. As 'h' gets smaller, errors gets larger. AB4-AM4 predictor corrector has greater errors than those from RK4. (a) h = 0.25000 x y(x) Y(x) error 0.00000 0.00000 0.00000 0.00000 0.25000 0.23525 0.23529 -0.00004 0.50000 0.39986 0.40000 -0.00014 0.75000 0.47979 0.48000 -0.00021 1.00000 0.49634 0.50000 -0.00366 1.25000 0.48363 0.48780 -0.00417 1.50000 0.45913 0.46154 -0.00241 1.75000 0.42951 0.43077 -0.00126 2.00000 0.39929 0.40000 -0.00071 h = 0.12500 x y(x) Y(x) error 0.00000 0.00000 0.00000 0.00000 0.25000 0.23529 0.23529 -0.00000 0.50000 0.39999 0.40000 -0.00001 0.75000 0.47984 0.48000 -0.00016 1.00000 0.49982 0.50000 -0.00018 1.25000 0.48769 0.48780 -0.00012 1.50000 0.46148 0.46154 -0.00006 1.75000
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Unformatted text preview: 0.43074 0.43077 -0.00003 2.00000 0.39999 0.40000 -0.00001 (b) h = 0.25000 x y(x) Y(x) error 0.00000 1.00000 1.00000 0.00000 0.25000 0.53125 0.52591 0.00534 0.50000 0.35547 0.35150 0.00397 0.75000 0.28955 0.28734 0.00221 1.00000 0.24755 0.26374 -0.01619 1.25000 0.23711 0.25505 -0.01794 1.50000 0.24921 0.25186 -0.00265 1.75000 0.25177 0.25068 0.00109 2.00000 0.24522 0.25025 -0.00503 h = 0.12500 x y(x) Y(x) error 0.00000 1.00000 1.00000 0.00000 0.25000 0.52613 0.52591 0.00022 0.50000 0.35086 0.35150 -0.00064 0.75000 0.28660 0.28734 -0.00074 1.00000 0.26325 0.26374 -0.00048 1.25000 0.25481 0.25505 -0.00025 1.50000 0.25174 0.25186 -0.00012 1.75000 0.25063 0.25068 -0.00005 2.00000 0.25023 0.25025 -0.00002...
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