我需要帮助实现我的工作四阶龙格-库塔方法来求解牛顿冷却定律。由于这个问题引入了时间(t),所以我对给定条件下的排名感到困惑。给出的内容如下:时间间隔从 t = 0 开始到 t = 20(以秒为单位),对象温度 = 300,环境温度 = 70,时间增量为 0.1,比例常数 = 0.19
public class RungeKutta {
public static double NewtonsCoolingLaw(double objectTemp,double ambientTemp)
{
double k = 0.19;
return -k * (objectTemp - ambientTemp);
}
public static void main(String[] args) {
double result = 0.0;
double initialObjectTemp = 300.0, givenAmbientTemp = 70.0;
double deltaX = (20.0 - 0)/10000;
for(double t = 0.0; t <= 20.0; t += .1)
{
double k1 = deltaX * NewtonsLaw(initialObjectTemp,givenAmbientTemp);
double k2 = deltaX * NewtonsLaw(initialObjectTemp + (deltaX/2.0),givenAmbientTemp + (k1/2.0));
double k3 = deltaX * NewtonsLaw(initialObjectTemp + (deltaX/2.0), givenAmbientTemp + (k2/2.0));
double k4 = deltaX * NewtonsLaw(initialObjectTemp + deltaX, givenAmbientTemp + k3);
givenAmbientTemp = givenAmbientTemp + (1.0/6.0) * (k1 + (2.0 * k2) + (2.0 * k3) + k4);
result = givenAmbientTemp;
}
System.out.println("The approx. object temp after 20 seconds is: " + result);
}
}
贝娄是我求解 ODE 的 RK4 方法。在下面的代码中,我求解 ODE y' = y - x 以近似 y(1.005),前提是 y(1) = 10 且 delta x = 0.001
public class RungeKutta {
public static double functionXnYn(double x,double y)
{
return y-x;
}
public static void main(String[] args) {
double deltaX = (1.005 - 0)/10000;
double y = 10.0;
double result = 0.0;
for(double x = 1.0; x <= 1.005; x = x + deltaX)
{
double k1 = deltaX * functionXnYn(x,y);
double k2 = deltaX * functionXnYn(x + (deltaX/2.0),y + (k1/2.0));
double k3 = deltaX * functionXnYn(x + (deltaX/2.0), y + (k2/2.0));
double k4 = deltaX * functionXnYn(x + deltaX, y + k3);
y = y + (1.0/6.0) * (k1 + (2.0 * k2) + (2.0 * k3) + k4);
result = y;
}
System.out.println("The value of y(1.005) is: " + result);
}
}
根据公式 T(t) = Ts + (T0 - Ts) * e^(-k*t) 我应该得到 75.1 的近似值来求解牛顿 DE。 Ts = 环境温度,T0 = 物体初始温度,t = 20(经过秒数),k = .19 比例常数
最佳答案
我猜测(但并不难)您要解决的 ODE 是
dT(t)/dt = -k*(T(t)-T_amb)
正如您所看到的,右侧并不直接取决于时间。
由于您没有尝试为系统编写代码,因此环境温度 T_amb
很可能是一个常量。因此,移动常量并使用一致的函数名称,并将 ODE 函数参数返回为格式时间,状态变量
public class RungeKutta {
public static double CoolingLaw(double time, double objectTemp)
{
double k = 0.19, ambientTemp = 70.0;
return -k * (objectTemp - ambientTemp);
}
public static void main(String[] args) {
double result = 0.0;
double objectTemp = 300.0;
double dt = 0.1
for(double t = 0.0; t <= 20.0; t += dt)
{
double k1 = dt * CoolingLaw(t, objectTemp);
double k2 = dt * CoolingLaw(t + (dt/2.0), objectTemp + (k1/2.0));
double k3 = dt * CoolingLaw(t + (dt/2.0), objectTemp + (k2/2.0));
double k4 = dt * CoolingLaw(t + dt, objectTemp + k3);
objectTemp = objectTemp + (1.0/6.0) * (k1 + (2.0 * k2) + (2.0 * k3) + k4);
result = objectTemp;
}
System.out.println("The approx. object temp after 20 seconds is: " + result);
}
}
关于java - 如何使用龙格-库塔法 (RK4) 求解牛顿冷却定律,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/56412486/