• 2022-06-08
    用泰勒展开方法证明二阶导数的三点数值微分公式[tex=15.643x2.357]79SmwT+8J9VTqKDgDEyFq0Tj5BoUEi422QW9VoAW6Ok0yerSj4rAakx7LOB3OlM1BFEPluEkBZ9R+5LwfammnGgqi2gWvkpqGfV0OqC8BhA8l/u6cuPe+ZS58kGBvRgtXhJ+UZRAyU1tmxJ7yw2wSYQrmujrzMS3CItLWp8XLs8qjgWFuVyIKZJ4vTt6MI2Z[/tex]的截断误差是 [tex=2.857x1.571]ExyfnU2xFXzFs0g31rJiYvgON3pnjHkgG7OI0zxEIOk=[/tex].
  • 证: 利用泰勒展开[tex=32.643x5.5]rZM5/OPAdr7aX+kNl9iwpOpYjL96T93bVI2xhW59LMTPgf/Nud8atuo37cvH7y++kNi8dKn8UraRbEHZ0cvGWUqf6Gm8oXYfygQdixgzDiPe/CO9eJ3wYnNNFBXREj+lFi/+nYXRIoDpIdBeWR8CX7y7VBHtab+z5jsN90rP9JqyE9ELbXAEdpYizHIcnPlXP9q3n3z4VbNbROn0m8udrF5Lszvs3FBHryqNZhHOjOX0w+mzckTKNNORjclVHUR+hdd/SwBzj7QSB5QJUShl7Hgd40rQcez+N3W7AFZGtWb+K/uB2tG+/J5gbJyJo+kXV4INHH1HJwL8FnL9fTTXN9YhumORChncB/q7vsp6qeGUrnk0EHRm1AN1r0uJ9F3OZ/Qp1Rck8NLYHCen6/ZBH278NncIv9kEXhAOgmNZJp8niOrBUmkD7JfHsv/UU7NG3XzgQyXkTedrMB8miL4K8LZGgRjJuj1qQzECfGkW/auXigKD7CZliI1ZqNcOXWohi2MoBAKGKKgQLgJpP09j9gRjsGcMjTUu2UhLcKzhzKlV7i1oROOHDd7NchXQ7IR2Q7ZBaxYot7fiR2k3PLwMPFuDNwNdrsIJ81VcjCt08lOVgaa69C8EHx4ep6K1Z6q2Db82OMvzc7bPlGFcyCZW5bkpxXvBJ0TWtQxfWXmlRrCA4e+ewklp46TH5PtO0WoGyW98/Wk00bQxvpwefXNj6w==[/tex]所以[tex=26.571x2.5]7P/7rm+mHaxpQWCskS9fvw1QSFfvaNcLqkzolPRLlAz3DxPR1NWToNDawVgbJ3Jk/LhezDeRHc8eHTaSgwIioOrS7Id0kLL+JLyslZYdFIXx0EyKxGkRT0+7AvoyZDXr6UarcMQx0KKlIkeaMOzl+a2s/R9de3DamkA/SzFaoS5vflP/aGCqYa9/7O2wVZy4wwicMOsaAjv/Vgirx/yevmn0le09NHyGEO/bHipOZ/M8UgPEv8hAjy30kCURcbgHkhvPtDnl9MrQncp87dhA692oS62qsDr2FRkLk7NRm+s=[/tex]即椎判误差为[tex=2.857x1.571]ExyfnU2xFXzFs0g31rJiYmvi8jI0PSNNB5ygDTcQIPk=[/tex].也可以利用插值法.构造埃尔米特插值问题如下:[tex=17.786x4.643]rZM5/OPAdr7aX+kNl9iwpAvJDV/dFMTc7rJZklb5BvgjB2PFe2oOYmFZ5YWTafb2cRRlUjETml1kKQXDExngRej3HOUoD18LmgwH2GANZ3Hv2FUE9wtWxXIX0Leq3d+wNiFUx8Z7hzlwitByHk3jqV0WpPNZn/lajFyEelWn8H9ueJ+H6yjFtgPFR/RFuUccOEjLaJvyDRsPet80h5Fp8yVFgXb8q4fc6WU9Ul56cHvsk+6+1epPihZgVtWgkSUj2K56kQuAAzbdvyVJrrVEbBHJIPgAigIniV3Iq5AgyZHTWnhdo6I3i9Eyv+B0cuKiaBto75P5gNWek4c7X69rkw==[/tex]利用基函数方法 (或其他方法) 可得[tex=25.0x10.071]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[/tex][br][/br]对上式求二阶导数,令[tex=2.286x1.0]qRhHolzQp43LlA0RxPD+Mg==[/tex]有[tex=26.286x8.5]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[/tex]

    内容

    • 0

      【单选题】请用地点定桩法在4分钟内记忆数字。 4 0 1 3 6 3 5 1 9 8 8 9 7 2 9 3 0 9 5 3 1 7 7 5 2 3 3 0 5 0 1 4 1 3 8 3 5 7 9 7 (5.0分) A. 已背 B. 未背

    • 1

      输出九九乘法表。 1 2 3 4 5 6 7 8 9 --------------------------------------------------------------------- 1*1=1 2*1=2 2*2=4 3*1=3 3*2=6 3*3=9 4*1=4 4*2=8 4*3=12 4*4=16 5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 6*1=6 6*2=12 6*3=18 6*4=24 6*5=30 6*6=36 7*1=7 7*2=14 7*3=21 7*4=28 7*5=35 7*6=42 7*7=49 8*1=8 8*2=16 8*3=24 8*4=32 8*5=40 8*6=48 8*7=56 8*8=64 9*1=9 9*2=18 9*3=27 9*4=36 9*5=45 9*6=54 9*7=63 9*8=72 9*9=81

    • 2

      list(range(-1,10,2)) A: [0, 2, 4, 6, 8, 10] B: [-1, 1, 3, 5, 7, 9] C: [0, 2, 4, 6, 8]

    • 3

      用泰勒展开方法证明二阶导数的三点数值微分公式[tex=15.643x2.357]79SmwT+8J9VTqKDgDEyFq0Tj5BoUEi422QW9VoAW6Ok0yerSj4rAakx7LOB3OlM1BFEPluEkBZ9R+5LwfammnGgqi2gWvkpqGfV0OqC8BhA8l/u6cuPe+ZS58kGBvRgtXhJ+UZRAyU1tmxJ7yw2wSYQrmujrzMS3CItLWp8XLs8qjgWFuVyIKZJ4vTt6MI2Z[/tex]的截断误差是 [tex=2.857x1.571]ExyfnU2xFXzFs0g31rJiYvgON3pnjHkgG7OI0zxEIOk=[/tex].

    • 4

      下面是图的拓扑排序的是?(多选)[img src="https://i1.chinesemooc.org/course/formula/201610/eb69927aaf8baae83211ee3fadf836e7.png"] A: 2 8 0 7 1 3 5 6 4 9 10 11 12 B: 2 8 7 0 6 9 11 12 10 1 3 5 4 C: 8 2 7 3 0 6 1 5 4 9 10 11 12 D: 8 2 7 0 6 9 10 11 12 1 3 5 4