Explicit Fixed-Step Continuous Solvers. Explicit solvers compute the value of a state at the next time step as an explicit function of the current values of both the state and the state derivative. Expressed mathematically for a fixed-step explicit solver:
where x is the state, Dx is a solver-dependent function that estimates the state derivative, h is the step size, and n indicates the current time step.
Simulink provides a set of explicit fixed-step continuous solvers. The solvers differ in the specific numerical integration technique that they use to compute the state derivatives of the model. The following table lists each solver and the integration technique it uses.
隐式固定步长连续求解器。隐式求解器根据隐函数的当前值和微分来求解下一步长的值。X是当前状态值，Dx是由步长决定的微分值，h是步长，n表示当前的时间步长。应该说simulink configuration 中的fixed步长就是指h，h是步长，和time step是什么关系？h和采样时间到底是什么关系呢？
| Solver | Integration Technique | Order of Accuracy |
|---|---|---|
| ode1 |
Euler's Method |
First |
| ode2 |
Heun's Method |
Second |
| ode3 |
Bogacki-Shampine Formula |
Third |
| ode4 |
Fourth-Order Runge-Kutta (RK4) Formula |
Fourth |
| ode5 |
Dormand-Prince (RK5) Formula |
Fifth |
| ode8 |
Dormand-Prince RK8(7) Formula |
Eighth |
The table lists the solvers in order of the computational complexity of the integration methods they use, from the least complex (ode1) to the most complex (ode8).
None of these solvers has an error control mechanism. Therefore, the accuracy and the duration of a simulation depends directly on the size of the steps taken by the solver.
求解器的阶数从最简单的ode1到最复杂的ode8，无一拥有错误控制机制，因此，他们的准确性和持续性取决于求解器的步长值h。
