Solving ODEs in MATLAB

1: Euler, ODE1Ode1实现了Euler的方法。它提供了ODE和ODES MATLAB套件的数值方法的介绍。指数增长和复合兴趣被用作示例。

2: Midpoint Method, ODE2ODE2 implements a midpoint method with two function evaluations per step. This method is twice as accurate as Euler's method. A nonlinear equation defining the sine function provides an example. An exercise involves implementing a trapezoid method.

3: Classical Runge-Kutta, ODE4ODE4 implements the classic Runge-Kutta method, the most widely used numerical method for ODEs over the past 100 years. Its major shortcoming is the lack of an error estimate. A simple model of the growth of a flame is an example that is used.

4:秩序,命名有限公司nventionsThe digits in the name of a MATLAB ODE solver reflect its order and resulting accuracy. A method is said to have order p if cutting the step size in half reduces the error in one step by a factor of two to the power p+1.

5：估计错误，ode23ODE23 compares 2nd and 3rd order methods to automatically choose the step size and maintain accuracy. It is the simplest MATLAB solver that has automatic error estimate and continuous interpolant. ODE23 is suitable for coarse accuracy requirements.

6: ODE45ODE45通常是ODE求解器中选择的功能。它比较了第四和第五阶方法以估计误差并确定步长。

7: Stiffness, ODE23s, ODE15sA problem is said to be stiff if the solution being sought varies slowly, but there are nearby solutions that vary rapidly, so the numerical method must take small steps to obtain satisfactory results. The flame model demonstrates stiffness.

8: Systems of EquationsAn ODE involving higher order derivatives is rewritten as a vector system involving only first order derivatives. The classic Van der Pol nonlinear oscillator is provided as an example. The VdP equation becomes stiff as the parameter is increased.

9: The MATLAB ODE SuiteMATLAB文档提供了两个图表，总结了MATLAB ODE SUITE中七个函数的功能。

10: Tumbling BoxThrow a rectangular box with sides of three different lengths into the air. You can get the box to tumble stably about its longest axis or its shortest axis. But if you try to make it tumble about it middle axis, you will find the motion is unstable.

11: Predator-Prey EquationsThe classic Lotka-Volterra model of predator-prey competition is a nonlinear system of two equations, where one species grows exponentially and the other decays exponentially in the absence of the other. The program "predprey" studies this model.

12：洛伦兹吸引者和混乱The Lorenz chaotic attractor was discovered by Edward Lorenz in 1963 when he was investigating a simplified model of atmospheric convection. It is a nonlinear system of three differential equations. The program "lorenzgui" studies this model.