MATLAB求解微分方程ppt课件

,求微分方程的解析解,dsolve(方程1,方程2,方程n,初始条件,自变量)记号:在表达微分方程时，用字母D表示求微分，D2、D3等表示求高阶微分.任何D后所跟的字母为因变量，自变量可以指定或由系统规则选定为确省,MATLAB命令：dsolve(Dx=1+x*x),结果：x=tan(t+C1),MATLAB命令：x,y=dsolve(D2x+2*Dx=x+2*y-exp(-t),.Dy=4*x+3*y+4*exp(-t);,结果：x=-6*t*exp(-t)+C1*exp(-t)+C2*exp(1+6(1/2)*t)+C3*exp(1-6(1/2)*t)y=6*t*exp(-t)-C1*exp(-t)+4*C2*exp(1+6(1/2)*t)+2*C2*exp(1+6(1/2)*t)*6(1/2)+4*C3*exp(1-6(1/2)*t)-2*C3*exp(1-6(1/2)*t)*6(1/2)+1/2*exp(-t),用Matlab求微分方程的数值解,t，x=solver（f,ts,x0,options）,STEP1令y1=x，y2=y1,STEP2建立M文件functiondy=vdp(t,y)dy=y(2);1000*(1-y(1)2)*y(2)-y(1);,STEP3调用MATLAB函数ODE15ST,Y=ode15s(vdp,03000,20);plot(T,Y(:,1),图形结果,使用匿名函数，STEP2和STEP3可以合并为vdp2=(t,y)y(2),1000*(1-y(1)2)*y(2)-y(1);%vdp2为匿名函数T,Y=ode15s(vdp2,0,3000,2,0);plot(T,Y(:,1),选定a=0.3，b=2,c=3初值x(0)=0,y(0)=0,z(0)=0,a=0.3;b=2;c=3;rossler=(t,y)-y(2)-y(3),y(1)+a*y(2),b+(y(1)-c)*y(3);ts=0100;x0=000;t,y=ode45(rossler,ts,x0);plot(t,y(:,1),r,t,y(:,2),b,t,y(:,3),g);figureplot3(y(:,1),y(:,2),y(:,3),微分方程求解时参数传递方法一,假设上例中参数a,b,c的值在运行时确定，我们可以这样建立函数文件rosslersolve.mfunctionrosslersolve(a,b,c)rossler1=(t,y,a,b,c)-y(2)-y(3),y(1)+a*y(2),b+(y(1)-c)*y(3);rossler2=(t,y)rossler1(t,y,a,b,c);ts=0100;x0=000;t,y=ode45(rossler2,ts,x0);plot3(y(:,1),y(:,2),y(:,3),Matlab命令行输入rosslersolve(0.2,2,3)求解参数a,b,c的值为0.2,2,3时的rossler方程,参数传递方法二,Lorenz=(t,y,beta,rho,sigma).-beta*y(1)+y(2)*y(3)-rho*(y(2)-y(3)-y(1)*y(2)+sigma*y(2)-y(3);ts=0,100;x0=001e-10;t,y=ode45(Lorenz,ts,x0,8/3,10,28)