我对此非常陌生，我在网上找不到任何帮助，如果之前已经回答过，我很抱歉。我试图在常微分方程上遵循这个简单的例子
using DifferentialEquations
f(t,u) = 1.01*u
u0=1/2
tspan = (0.0,1.0)
prob = ODEProblem(f,u0,tspan)
sol = solve(prob,Tsit5(),reltol=1e-8,abstol=1e-8)
using Plots
plot(sol,linewidth=5,title="Solution to the linear ODE with a thick line",
xaxis="Time (t)",yaxis="u(t) (in ?m)",label="My Thick Line!") # legend=false
plot!(sol.t, t->0.5*exp(1.01t),lw=3,ls=:dash,label="True Solution!")
但是当我调用solve函数时出现这个错误
MethodError: no method matching f(::Float64, ::DiffEqBase.NullParameters, ::Float64)
Closest candidates are:
f(::Any, ::Any) at /Users/diogomiguez/.julia/pluto_notebooks/Cute science.jl#==#dbde1a90-407c-11eb-15ad-394234f71852:1
(::DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing})(::Float64, ::Vararg{Any,N} where N)@diffeqfunction.jl:248
initialize!(::OrdinaryDiffEq.ODEIntegrator{OrdinaryDiffEq.CompositeAlgorithm{Tuple{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},false,Float64,Nothing,Float64,DiffEqBase.NullParameters,Float64,Float64,Float64,Array{Float64,1},OrdinaryDiffEq.ODECompositeSolution{Float64,1,Array{Float64,1},Nothing,Nothing,Array{Float64,1},Array{Array{Float64,1},1},DiffEqBase.ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},OrdinaryDiffEq.CompositeAlgorithm{Tuple{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Array{Float64,1},Array{Array{Float64,1},1},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,DiffEqBase.TimeDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqBase.UDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},Float64,Float64,DiffEqBase.DefaultLinSolve}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,DiffEqBase.TimeDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqBase.UDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},Float64,Float64,DiffEqBase.DefaultLinSolve}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),DiffEqBase.CallbackSet{Tuple{},Tuple{}},typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN),typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE),typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK),DataStructures.BinaryHeap{Float64,Base.Order.ForwardOrdering},DataStructures.BinaryHeap{Float64,Base.Order.ForwardOrdering},Nothing,Nothing,Int64,Tuple{},Tuple{},Tuple{}},Float64,Float64,Nothing,OrdinaryDiffEq.DefaultInit}, ::OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64})@low_order_rk_perform_step.jl:565
initialize!(::OrdinaryDiffEq.ODEIntegrator{OrdinaryDiffEq.CompositeAlgorithm{Tuple{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},false,Float64,Nothing,Float64,DiffEqBase.NullParameters,Float64,Float64,Float64,Array{Float64,1},OrdinaryDiffEq.ODECompositeSolution{Float64,1,Array{Float64,1},Nothing,Nothing,Array{Float64,1},Array{Array{Float64,1},1},DiffEqBase.ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},OrdinaryDiffEq.CompositeAlgorithm{Tuple{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Array{Float64,1},Array{Array{Float64,1},1},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,DiffEqBase.TimeDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqBase.UDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},Float64,Float64,DiffEqBase.DefaultLinSolve}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,DiffEqBase.TimeDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqBase.UDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},Float64,Float64,DiffEqBase.DefaultLinSolve}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),DiffEqBase.CallbackSet{Tuple{},Tuple{}},typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN),typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE),typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK),DataStructures.BinaryHeap{Float64,Base.Order.ForwardOrdering},DataStructures.BinaryHeap{Float64,Base.Order.ForwardOrdering},Nothing,Nothing,Int64,Tuple{},Tuple{},Tuple{}},Float64,Float64,Nothing,OrdinaryDiffEq.DefaultInit}, ::OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,DiffEqBase.TimeDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqBase.UDerivativeWrapper{DiffEqBase.ODEFunction{false,typeof(Main.workspace465.f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},Float64,Float64,DiffEqBase.DefaultLinSolve}},OrdinaryDiffEq.AutoSwitchCache{OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.Rosenbrock23{0,false,DiffEqBase.DefaultLinSolve,DataType},Rational{Int64},Int64}})@composite_perform_step.jl:39
#__init#399(::Tuple{}, ::Tuple{}, ::Tuple{}, ::Nothing, ::Bool, ::Bool, ::Bool, ::Bool, ::Nothing, ::Bool, ::Bool, ::Float64, ::Nothing, ::Float64, ::Bool, ::Bool, ::Rational{Int64}, ::Nothing, …julia ×1