vdptest.asv

(有源代码)数值分析作业,本文主要包括两个部分,第一部分是常微分方程(ODE)的三个实验题,第二部分是有关的拓展讨论,包括高阶常微分的求解和边值问题的求解(BVP).文中的算法和算例都是基于Matla

% function vdptest
tspan = [0, 20];
y0 = [2; 0];
Mu = 1;
[t,y] = ode45(@vanderpoldemo, tspan, y0,[],Mu);

% Plot of the solution
figure(1)
plot(t,y(:,1))
xlabel('t')
ylabel('solution y')
title('van der Pol Equation, \mu = 1')

figure(2)
plot(y(:,1),y(:,2))
xlabel('diff(y)')
ylabel('diff(y,2)')
title('phase figure')

%stiff problem
tspan = [0, 3000];
y0 = [2; 0];
Mu = 1000;
[t,y] = ode15s(@vanderpoldemo, tspan, y0,[],Mu);


figure(3)
plot(t,y(:,1))
title('van der Pol Equation, \mu = 1000,solved with ode15s')
axis([0 3000 -3 3])
xlabel('t')
ylabel('solution y')