26 lines
1.0 KiB
Python
26 lines
1.0 KiB
Python
#经典R-K，龙格-库塔法
|
||
def ClassicRK(x0,y0,h,xk,fxy):
|
||
k1=k2=k3=k4=0
|
||
result = [(x0,y0)]
|
||
while x0<=xk:
|
||
k1 = fxy(x0,y0)
|
||
k2 = fxy(x0+h/2,y0+h*k1/2)
|
||
k3 = fxy(x0+h/2,y0+h*k2/2)
|
||
k4 = fxy(x0+h,y0+h*k3)
|
||
y0 += h*(k1+2*k2+2*k3+k4)/6
|
||
x0 += h
|
||
result.append((x0,y0))
|
||
return result
|
||
|
||
#把下面参数换成题干的#################
|
||
if __name__=="__main__":
|
||
x0 = 0 #x的左边界换成题干里面的#################
|
||
y0 = -1 #y的初始值换成题干里面的#################
|
||
fxy = lambda x,y: x + y #f(x,y)换成题干里面的#################
|
||
real_fx = lambda x: -x-1 #真实函数换成题干里面的#################
|
||
h = 0.1 #步长换成题干里面的#################
|
||
xk = 2 #x的右边界换成题干里面的#################
|
||
result = ClassicRK(x0, y0, h, xk, fxy)
|
||
print("x\ty\t\treal_y\t\t\t误差")
|
||
for x, y in result:
|
||
print(f"{x:.2f}\t{y:.10f}\t\t{real_fx(x):.10f}\t\t\t{abs(y - real_fx(x))}") |