差分方程及微分方程数值解(1)

《差分方程及微分方程数值解(1)》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、东南大学《数学实验》报告学号07106125姓名张国均成绩实验内容：差分方程及微分方程数值解一实验目的熟悉迭代法及微分方程数值方法二预备知识（1）了解差分方程稳定性、周期分解、混沌等相关知识（2）了解欧拉方法、龙格-库特方法。三实验内容与要求（一）Volterra方程数值解方程：程序：函数：functiondx=fun(t,x)a=2;b=1;c=1;d=2;dx=[a*x(1)-b*x(1)*x(2);-c*x(2)+d*x(1)*x(2)];相图：holdonfork=1:5ts=0:0.01:10;x0=[1,0.5*k];5[t,x]=ode45(

2、'fun',ts,x0);plot(x(:,1),x(:,2))endxlabel('x');ylabel('y');holdoff轨迹图：holdonts=0:0.01:10;x0=[11];[t,x]=ode45('fun',ts,x0);plot(t,x(:,1),'y');plot(t,x(:,2),'r');holdoff5（二）差分阻滞增长模型（）（1）稳定情况程序：functionx=block(b,x0)ifnargin<2x0=0.5;endx=x0;n=1:10000;fori=2:10000x(i)=b*x(i-1)*(1-x(i-1

3、));endplot(n,x,'.');5稳定性分析非零平衡点都是稳定平衡点命令与结果（图）block(1.6);稳定性分析非零平衡点都是稳定平衡点命令与结果（图）block(2.2);（2）不稳定情况稳定性分析命令与结果（图）block(3.3);稳定性分析命令与结果（图）block(3.63);5（3）倍周期分解求稳定平衡点两个平衡点：0.47940.8236（2）数值结果0.50000.82500.47640.82320.48040.82370.47920.82360.47950.82360.47940.82360.47940.82360.47940

4、.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.82360.47940.8236求稳定平衡点四个平衡点：0.50090.87500.38280.8269数值结果0.50000.

5、87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690

6、.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.38280.82690.50090.87500.3828

7、0.82690.50090.87500.38280.82695