def METHOD_NAME(self,beta,alpha):
    AD = self.get_left_matrix(beta,alpha)
    b = self.get_right_vector()
    self.uh = self.space.function()
    self.uh[:] = spsolve(AD, b)
    ls = {'A':AD, 'b':b, 'solution':self.uh.copy()}
    return ls # return the linear system