给你个例子:
du/dx = v;
dv/dx = x+(1-x/5)*u;
初始条件:x=[1, 3], u(1)=2, v(3)=0.5
1stOpt求解:
- Variable x=[1,3], u=[2,], v=[,0.5];
- Plot x[x], u, v;
- ODEFunction u' = v;
- v'=x+(1-x/5)*u;
复制代码
边值估算:
v(x=1): -3.51415168673288
算法: 龙格-库塔-费尔博格法(Runge-Kutta-Fehlberg Method)
结果:
x u(x) v(x) u'(x) v'(x)
1 2 -3.51415168673288 -3.51415168673288 2.6
3 -1.05560321447593 0.500000000000001 0.500000000000001 2.57775871420963
结果过程:
x u(x) v(x) u'(x) v'(x)
1 2 -3.51415168673288 -3.51415168673288 2.6
1.1 1.66123053011661 -3.26464084967581 -3.26464084967581 2.39575981349096
1.2 1.34644512324993 -3.03394087703253 -3.03394087703253 2.22329829366995
1.3 1.05391690309206 -2.81901285096046 -2.81901285096046 2.07989850828813
1.4 0.782209899214626 -2.61707176268615 -2.61707176268615 1.96319112743453
1.5 0.530155316619517 -2.42555408211952 -2.42555408211952 1.87110872163366
1.6 0.296830827472975 -2.24208964559251 -2.24208964559251 1.80184496268162
1.7 0.0815424773574236 -2.064477407615 -2.064477407615 1.7538180350559
1.8 -0.116191160344767 -1.89066466633647 -1.89066466633647 1.72563765737935
1.9 -0.29665291215347 -1.71872942831437 -1.71872942831437 1.71607519446485
2 -0.459939313531547 -1.54686562649315 -1.54686562649315 1.72403641188107
2.1 -0.605971572038914 -1.37337094687938 -1.37337094687938 1.74853648821743
2.2 -0.734505434750786 -1.19663705501167 -1.19663705501167 1.78867695653956
2.3 -0.845140190757058 -1.01514204360741 -1.01514204360741 1.84362429699119
2.4 -0.937327023010404 -0.827444948258091 -0.827444948258091 1.91258994803459
2.5 -1.01037690956979 -0.63218219919461 -0.63218219919461 1.9948115452151
2.6 -1.06346826197935 -0.428065894333176 -0.428065894333176 2.08953523424991
2.7 -1.09565447775007 -0.213883792360387 -0.213883792360387 2.19599894023497
2.8 -1.10587157432361 0.0114990652087905 0.0114990652087905 2.31341650729762
2.9 -1.09294606316761 0.249137187037573 0.249137187037573 2.4409626534696
3 -1.05560321447593 0.500000000000001 0.500000000000001 2.57775871420963