数值分析上机题课后课后复习全部-东南大学

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7 0.600000 2.467100 2.467105 0.000005 ------------------------------------------------------------- 8 0.700000 2.233799 2.233805 0.000006 ------------------------------------------------------------- 9 0.800000 1.984123 1.984127 0.000004 ------------------------------------------------------------- 10 0.900000 1.735107 1.735107 -0.000000 ------------------------------------------------------------- 11 1.000000 1.500006 1.500000 -0.000006 ------------------------------------------------------------- 12 1.100000 1.287013 1.287001 -0.000011 ------------------------------------------------------------- 13 1.200000 1.099722 1.099707 -0.000015 ------------------------------------------------------------- 14 1.300000 0.938397 0.938380 -0.000018 ------------------------------------------------------------- 15 1.400000 0.801300 0.801282 -0.000018 ------------------------------------------------------------- （2）AB4法 >> AB4 请输入初始x值：x0=0 请输入初值条件：y（x0）=3 请输入计算步数：N=15 请输入步长：h=0.1 i xi yi y(xi) y(xi)-yi ------------------------------------------------------------- 1 0.000000 3.000000 3.000000 0.000000 ------------------------------------------------------------- 2 0.100000 2.997003 2.997003 0.000000 ------------------------------------------------------------- 3 0.200000 2.976190 2.976190 0.000000 ------------------------------------------------------------- 4 0.300000 2.921129 2.921130 0.000001 ------------------------------------------------------------- 5 0.400000 2.818389 2.819549 0.001160 ------------------------------------------------------------- 6 0.500000 2.664672 2.666667 0.001994 ------------------------------------------------------------- 7 0.600000 2.465203 2.467105 0.001903 ------------------------------------------------------------- 8 0.700000 2.233079 2.233805 0.000726 ------------------------------------------------------------- 9 0.800000 1.984951 1.984127 -0.000824 ------------------------------------------------------------- !-

10 0.900000 1.737043 1.735107 -0.001936 ------------------------------------------------------------- 11 1.000000 1.502195 1.500000 -0.002195 ------------------------------------------------------------- 12 1.100000 1.288763 1.287001 -0.001762 ------------------------------------------------------------- 13 1.200000 1.100724 1.099707 -0.001017 ------------------------------------------------------------- 14 1.300000 0.938710 0.938380 -0.000331 ------------------------------------------------------------- 15 1.400000 0.801135 0.801282 0.000147 ------------------------------------------------------------- （3）AB4-AM4预测校正法 >> AB4AM4 请输入初始x值：x0=0 请输入初值条件：y（x0）=3 请输入计算步数：N=15 请输入步长：h=0.1 i xi yi y(xi) y(xi)-yi ------------------------------------------------------------- 1 0.000000 3.000000 3.000000 0.000000 ------------------------------------------------------------- 2 0.100000 2.997003 2.997003 0.000000 ------------------------------------------------------------- 3 0.200000 2.976190 2.976190 0.000000 ------------------------------------------------------------- 4 0.300000 2.921129 2.921130 0.000001 ------------------------------------------------------------- 5 0.400000 2.819678 2.819549 -0.000130 ------------------------------------------------------------- 6 0.500000 2.666876 2.666667 -0.000209 ------------------------------------------------------------- 7 0.600000 2.467252 2.467105 -0.000147 ------------------------------------------------------------- 8 0.700000 2.233731 2.233805 0.000073 ------------------------------------------------------------- 9 0.800000 1.983787 1.984127 0.000340 ------------------------------------------------------------- 10 0.900000 1.734607 1.735107 0.000500 ------------------------------------------------------------- 11 1.000000 1.499516 1.500000 0.000484 ------------------------------------------------------------- 12 1.100000 1.286657 1.287001 0.000344 ------------------------------------------------------------- !-

13 1.200000 1.099533 1.099707 0.000174 ------------------------------------------------------------- 14 1.300000 0.938343 0.938380 0.000037 ------------------------------------------------------------- 15 1.400000 0.801327 0.801282 -0.000045 ------------------------------------------------------------- （4）带改进的AB4-AM4预测校正法 >> AB4AM4plus 请输入初始x值：x0=0 请输入初值条件：y（x0）=3 请输入计算步数：N=15 请输入步长：h=0.1 i xi yi y(xi) y(xi)-yi ------------------------------------------------------------- 1 0.000000 3.000000 3.000000 0.000000 ------------------------------------------------------------- 2 0.100000 2.997003 2.997003 0.000000 ------------------------------------------------------------- 3 0.200000 2.976190 2.976190 0.000000 ------------------------------------------------------------- 4 0.300000 2.921129 2.921130 0.000001 ------------------------------------------------------------- 5 0.400000 2.819588 2.819549 -0.000039 ------------------------------------------------------------- 6 0.500000 2.666713 2.666667 -0.000046 ------------------------------------------------------------- 7 0.600000 2.467097 2.467105 0.000008 ------------------------------------------------------------- 8 0.700000 2.233682 2.233805 0.000122 ------------------------------------------------------------- 9 0.800000 1.983885 1.984127 0.000242 ------------------------------------------------------------- 10 0.900000 1.734808 1.735107 0.000299 ------------------------------------------------------------- 11 1.000000 1.499732 1.500000 0.000268 ------------------------------------------------------------- 12 1.100000 1.286821 1.287001 0.000181 ------------------------------------------------------------- 13 1.200000 1.099622 1.099707 0.000085 ------------------------------------------------------------- 14 1.300000 0.938367 0.938380 0.000012 ------------------------------------------------------------- 15 1.400000 0.801311 0.801282 -0.000029 ------------------------------------------------------------- !-

6.4结果分析

从每一种方法的计算误差可以看出，精度由高到低依次是：RK4法、改进的AB4-AM4法、AB4-AM4法、AB4法。