如何在Matlab中绘制非线性微分方程 [英] How do you plot nonlinear differential equations in matlab

问题描述

Dx=y
Dy=-k*y-x^3+9.8*cos(t)
inits=('x(0)=0,y(0)=0')

这些是我想绘制的微分方程.

these are the differential equations that I wanted to plot.

首先，我尝试求解微分方程，然后绘制图形.

first, I tried to solve the differential equation and then plot the graph.

Dsolve('Dx=y','Dy=-k*y-x^3+9.8*cos(t)', inits)

但是，这种系统没有明确的解决方案.

like this, however, there was no explicit solution for this system.

现在我被卡住了:(

如何在不求解方程的情况下绘制该系统?

how can you plot this system without solving the equations?

推荐答案

首先定义要求解的微分方程.它必须是一个带有两个参数的函数-当前时间t和当前位置x，并返回列向量.代替x和y，我们将使用x(1)和x(2).

First define the differential equation you want to solve. It needs to be a function that takes two arguments - the current time t and the current position x, and return a column vector. Instead of x and y, we'll use x(1) and x(2).

k = 1;
f = @(t,x) [x(2); -k * x(2) - x(1)^3 + 9.8 * cos(t)];

定义要解决的时间范围以及初始条件:

Define the timespan you want to solve over, and the initial condition:

tspan = [0, 10];
xinit = [0, 0];

现在使用ode45数值求解方程:

Now solve the equation numerically using ode45:

ode45(f, tspan, xinit)

这将导致该图:

如果要及时获取解决方案的值，则只需询问一些输出参数即可:

If you want to get the values of the solution at points in time, then just ask for some output arguments:

[t, y] = ode45(f, tspan, xinit);

您可以通过这样做

plot(y(:,1), y(:,2)), xlabel('x'), ylabel('y'), grid

这将导致以下情节

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