ODESolverMethod {Microsoft.VisualBasic.Math.Calculus.Dynamics}

.NET clr documentation

ODESolverMethod

Description

The available integration algorithms of the ODEs dynamics system. (常微分方程组可用的积分算法)

方法	阶数	类型	适用
ODESolverMethod.Euler	1	显式固定步长	教学 / 快速原型
ODESolverMethod.RK2	2	显式固定步长	一般用途
ODESolverMethod.Gill	4	显式固定步长	长时程积分(舍入误差累积较小)
ODESolverMethod.RK4	4	显式固定步长	默认推荐
ODESolverMethod.ABM4	4	显式多步预测-校正	光滑非刚性问题的批量仿真
ODESolverMethod.BackwardEuler	1	隐式(L-稳定)	强刚性问题
ODESolverMethod.Trapezoidal	2	隐式(A-稳定)	一般刚性问题
ODESolverMethod.BDF2	2	隐式	刚性问题
ODESolverMethod.RosenbrockROS2	2	线性隐式(L-稳定)	刚性问题(无需 Newton 迭代)
ODESolverMethod.RK23	3(2)	自适应显式	粗略/低频仿真
ODESolverMethod.RK45	5(4)	自适应显式	高精度通用
ODESolverMethod.Verlet	2	辛几何	哈密顿系统(位置/动量可分裂)
ODESolverMethod.Yoshida4	4	辛几何	哈密顿系统(高精度能量守恒)

Declare

            
# namespace Microsoft.VisualBasic.Math.Calculus.Dynamics
export class ODESolverMethod extends Enum {
   # Forward Euler method, 1st order.(前向欧拉法)
   Euler: ODESolverMethod = 0;

   # The improved Euler (Heun) method, 2nd order.(改进欧拉法)
   RK2: ODESolverMethod = 1;

   # The 4-stage 4th order Gill method, it has a smaller round-off accumulation than RK4. (四阶 Gill 方法，舍入误差累积较小)
   Gill: ODESolverMethod = 2;

   # The classical 4-stage 4th order Runge-Kutta method.(经典四阶龙格库塔法)
   RK4: ODESolverMethod = 3;

   # The 4th order Adams-Bashforth-Moulton predictor-corrector method.(四阶阿当姆斯预测-校正法)
   ABM4: ODESolverMethod = 4;

   # The implicit backward Euler method (BDF1), L-stable.(隐式后向欧拉法)
   BackwardEuler: ODESolverMethod = 5;

   # The implicit trapezoidal rule (Crank-Nicolson), A-stable.(隐式梯形法)
   Trapezoidal: ODESolverMethod = 6;

   # The 2nd order backward differentiation formula, it is suitable for the stiff problems. (二阶后向微分公式)
   BDF2: ODESolverMethod = 7;

   # The 2-stage 2nd order L-stable Rosenbrock method (linearly implicit).(二阶线性隐式方法)
   RosenbrockROS2: ODESolverMethod = 8;

   # The Bogacki-Shampine 3(2) adaptive step size method.(自适应 RK23 方法)
   RK23: ODESolverMethod = 9;

   # The Dormand-Prince 5(4) adaptive step size method.(自适应 RK45 方法)
   RK45: ODESolverMethod = 10;

   # The 2nd order Stormer-Verlet symplectic method.(二阶辛几何算法)
   Verlet: ODESolverMethod = 11;

   # The 4th order Yoshida composition of the Stormer-Verlet method.(四阶吉田分解)
   Yoshida4: ODESolverMethod = 12;

}

        

.NET clr type reference tree

1. this class extends from Enum class: Enum
2. use by field member Euler: ODESolverMethod
3. use by field member RK2: ODESolverMethod
4. use by field member Gill: ODESolverMethod
5. use by field member RK4: ODESolverMethod
6. use by field member ABM4: ODESolverMethod
7. use by field member BackwardEuler: ODESolverMethod
8. use by field member Trapezoidal: ODESolverMethod
9. use by field member BDF2: ODESolverMethod
10. use by field member RosenbrockROS2: ODESolverMethod
11. use by field member RK23: ODESolverMethod
12. use by field member RK45: ODESolverMethod
13. use by field member Verlet: ODESolverMethod
14. use by field member Yoshida4: ODESolverMethod

---