29 lines
1.1 KiB
Python
29 lines
1.1 KiB
Python
import math
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#经典R-K，龙格-库塔法
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def ClassicRK(x0,y0,h,xk,fxy):
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k1=k2=k3=k4=0
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result = [(x0,y0)]
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while x0<=xk:
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k1 = fxy(x0,y0)
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k2 = fxy(x0+h/2,y0+h*k1/2)
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k3 = fxy(x0+h/2,y0+h*k2/2)
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k4 = fxy(x0+h,y0+h*k3)
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y0 += h*(k1+2*k2+2*k3+k4)/6
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x0 += h
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result.append((x0,y0))
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return result
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if __name__=="__main__":
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##########################################################################
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x0 = 0 # x的初始值（左边界）换成题干里面的#################
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y0 = -1 # y的初始值换成题干里面的#################
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fxy = lambda x,y: x + y #f(x,y)换成题干里面的#################
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real_fx = lambda x: -x-1 #真实函数换成题干里面的#################
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h = 0.1 #步长换成题干里面的#################
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xk = 2 #x的右边界换成题干里面的#################
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result = ClassicRK(x0, y0, h, xk, fxy)
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print("x\ty\t\treal_y\t\t\t误差")
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for x, y in result:
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print(f"{x:.2f}\t{y:.10f}\t\t{real_fx(x):.10f}\t\t\t{abs(y - real_fx(x)):.5f}") |