- 我要求解一阶（相对于时间t)微分方程组，它同时依赖于一些参数，比如p，我想对它的解的绝对值相对于参数p求数值定积分，我写了一个程序，但是始终报错，不知道错误在何处，请高人指点一二。下面是元代码：
using DifferentialEquations
using QuadGK
using ForwardDiff
# Constants
g = 0.0045
Δ0 = 0
Ω = 5
ϕ = 0
# Define B3 function
function B3(t, q, α, g, Δ0)
return -q - g * t - (Δ0 - α * t)
end
# Define the system of ODEs
function odefunc!(du, u, p, t)
fp, f3, fm = u
q, α, Ω, ϕ = p
du[1] = Ω/2 * exp(1im * ϕ) - 1im * B3(t, q, α, g, Δ0) * fp + Ω/2 * exp(-1im * ϕ) * fp^2
du[2] = B3(t, q, α, g, Δ0) + 2 * 1im * fp * Ω / 2 * exp(-1im * ϕ)
du[3] = exp(-1im * f3) * Ω / 2 * exp(-1im * ϕ)
end
# Initial conditions and time span
u0 = [0.0, 0.0, 0.0] # Initial conditions for fp, f3, fm
tspan = (0.0, 10.0)
# Function to solve the ODE for a given parameter p
function solve_ode(p)
prob = ODEProblem(odefunc!, u0, tspan, p)
sol = solve(prob, Tsit5())
return sol
end
# Function to compute the integral of the solution with respect to p
function integrate_solution(p_values, tf, α, Ω, ϕ)
integrand(p) = begin
sol = solve_ode([p, α, Ω, ϕ])
abs(sol(tf)[1]) # Assuming you want to integrate the first component
end
result, _ = quadgk(integrand, p_values[1], p_values[end])
return result
end
# Example usage
p_values = [0.0, 3.0] # Range of p values
tf = 10.0 # Final time
result = integrate_solution(p_values, tf, g, Ω, ϕ)
println("Result: ", result)