Solve a system of non-linear equations in Python (scipy.optimize.fsolve)

[drudox]

yes it is an Implicit Runge Kutta method !! I've already done this ! and actually now my solve methods is this :

d

ef solve(self):
        '''
              perform Implicit RK4 scheme 
        '''
        self.time , self.u = self.dydt.createArray()
        print("Running Implicit RK 4th order") 
        
        for i in range(len(self.time)-1):

            def equations(variable):
                k1, k2 = variable
                f1 = -k1 + self.f(self.time[i]+ (0.5+np.sqrt(3)/6)* self.dt , self.u[i]+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                f2 = -k2 + self.f(self.time[i]+ (0.5-np.sqrt(3)/6)* self.dt , self.u[i]+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                return np.array([f1,f2]).ravel() #.reshape(2,)  
                        
                
            k1 , k2 = fsolve(equations,(self.u[i],self.u[i]))
            
            self.u[i+1] = self.u[i] + self.dt/2* (k1 + k2)
 
        print('... Done!')

this works fine when I deal with a ODE single equations ... but doesn't works when I deal with system of ODE ... may you help me to find the right way to proceed ?

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I declare the equation inside the for loop (where else ?) because k1 , k2 are function of

self.time[i], self.u[i]