内插后用ode45求解ODE [英] Solving an ODE with ode45 after interpolating

问题描述

我正在使用以下代码，找不到错误的地方:

I am working with the following code and can't find what is wrong:

xx = 0:1/50:1;
v = 3.*exp(-xx)-0.4*xx;
xq = xx;
vq = @(xq) interp1(xx,v,xq);

tspan = 0:1/50:1;
x0 = 3;
[~, y2] = ode45(@(t,x)vq(x), tspan, x0);

我知道了y2 = [3;NAN;NAN;NAN,.....].但是，当我在调用ode45之前绘制两个方程式时，我发现它们相等，这不足为奇.

I get that y2 = [3;NAN;NAN;NAN,.....]. Yet, when I plot both equations before calling ode45, I get that they are equal, which is not a surprise.

当我计算时:

f = @(t,r) 3.*exp(-r)-0.4*r;
[~, y] = ode45(f,tspan,x0);

它工作正常.但是我需要证明，如果插值，我可以获得相同的结果.为什么这样不起作用?

it works fine. But I need to show that I can get the same results if I interpolate. Why is that not working?

推荐答案

您将获得NaN，因为这是

You get NaN because that is the default returned by interp1 for values outside of the interval spanned by xx. In you case, xx only varies from 0 to 1. But your initial condition is at 3. If you're going to use interpolation you need start inside of the interval defined by your data and make sure you stay there. For example, if you simply change your initial condition:

xx = 0:1/50:1;
v = 3.*exp(-xx)-0.4*xx;
xq = xx;
vq = @(xq) interp1(xx,v,xq);

tspan = 0:1/50:1;
x0 = 0.1;
[t, y2] = ode45(@(t,x)vq(x), tspan, x0);

f = @(t,r) 3.*exp(-r)-0.4*r;
[t, y] = ode45(f,tspan,x0);

figure;
subplot(211)
plot(t,y,'b',t,y2,'r--')
subplot(212)
plot(t,abs(y-y2))
xlabel('t')
ylabel('Absolute Error')

即使在这种初始条件下，由于指数增长，系统状态在特定点也会离开您的[0，1]间隔，并且y2将变为NaN.如果愿意，可以告诉interp1使用实际推断但是.

Even with this initial condition, because of the exponential growth, at a certain point the state of the system leaves your [0, 1] interval and y2 will become NaN. You can tell interp1 to use actual extrapolation if you prefer though.

这篇关于内插后用ode45求解ODE的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！