Python 让函数调用方程

发布于03月30日

我正在创建一个函数来创建一个微分方程的近似解，使用欧拉方法. 我可以让代码工作，但遇到了麻烦时，试图将其转换为一个函数. 也就是说，我很难让我的函数正确调用公式.

This original code worked well:

#define your inital values
y = 1
x = 0
#h represents step size (incremental shift over the directional field)
h = 0.1

solutions = []
x_values = []

#generates a list of 10 solutions, increase the number in the range to get more solutions
for s in range (0, 10):
    #enter your differential equation 
    diff_eq = x+y
    #Euler's method to approximate the solutions
    s = y + h*(diff_eq)
    solutions.append(s)
    #replace initial values with the new values
    y = s
    x = x + h
    #create a list of the x values
    x_values.append(x)

#creating a dataframe from the solutions
Euler_values = pd.DataFrame(list(zip(x_values, solutions)), columns = ['xₙ', 'yₙ'])
#create an index for the dataframe starting at one and increasing by one 
Euler_values.index = Euler_values.index + 1
Euler_values.rename_axis('n', inplace = True)
Euler_values

This is the start of turning the above code into a function:

#eulers method to approximate the solutions function
def eulers_method(x, y, diff_eq, h, n):
    #empty solution and x_value lists to be used in the euler function
    solutions = []
    x_values = []
    
    for s in range (0, n):
        # eq = diff_eq <-- this does not work
        # if I call the equation here it does work, but I want it to be entered into the function
        eq = x + y
        s = y + h*(eq)
        #replace initial values with the new values and adds them to the solution and x_value lists
        y = s
        solutions.append(s)
        x = x + h
        x_values.append(x)
    #creates a dataframe from the solutions
    Euler_values = pd.DataFrame(list(zip(x_values, solutions)), columns = ['xₙ', 'yₙ'])
    #creates an index for the dataframe starting at one and increasing by one 
    Euler_values.index = Euler_values.index + 1
    Euler_values.rename_axis('n', inplace = True)
    return Euler_values    

#enter an initial x value, initial y value, the differential equation, the step size, and the number of solutions to generate
# the diff_eq entry is giving me trouble
eulers_method(0,1, x+y, 0.1, 10)

def eulers_method(x, y, diff_eq, h, n): #empty solution and x_value lists to be used in the euler function solutions = [] x_values = [] for s in range (0, n): # compute the function eq = diff_eq(x, y) s = y + h*(eq) #replace initial values with the new values and adds them to the solution and x_value lists y = s solutions.append(s) x = x + h x_values.append(x) #creates a dataframe from the solutions Euler_values = pd.DataFrame(list(zip(x_values, solutions)), columns = ['xₙ', 'yₙ']) #creates an index for the dataframe starting at one and increasing by one Euler_values.index = Euler_values.index + 1 Euler_values.rename_axis('n', inplace = True) return Euler_values #enter an initial x value, initial y value, the differential equation, the step size, and the number of solutions to generate eulers_method(0, 1, lambda x, y:x+y, 0.1, 10)

xₙ yₙ n 1 0.1 1.100000 2 0.2 1.220000 3 0.3 1.362000 4 0.4 1.528200 5 0.5 1.721020 6 0.6 1.943122 7 0.7 2.197434 8 0.8 2.487178 9 0.9 2.815895 10 1.0 3.187485

def eulers_method(x, y, diff_eq, h, n): #empty solution and x_value lists to be used in the euler function solutions = [] x_values = [] for s in range (0, n): # compute the function eq = eval(diff_eq) s = y + h*(eq) #replace initial values with the new values and adds them to the solution and x_value lists y = s solutions.append(s) x = x + h x_values.append(x) #creates a dataframe from the solutions Euler_values = pd.DataFrame(list(zip(x_values, solutions)), columns = ['xₙ', 'yₙ']) #creates an index for the dataframe starting at one and increasing by one Euler_values.index = Euler_values.index + 1 Euler_values.rename_axis('n', inplace = True) return Euler_values #enter an initial x value, initial y value, the differential equation, the step size, and the number of solutions to generate eulers_method(0, 1, 'x+y', 0.1, 10)

Python 让函数调用方程

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