微分方程式を解きたい

前提・実現したいこと

微分方程式をJuliaで解く。コード中の sol = solve(prob)からうまくいかない。

発生している問題・エラーメッセージ

ERROR: MethodError: no method matching f(::Float64, ::DiffEqBase.NullParameters, ::Float64)
Closest candidates are:
  f(::Any, ::Any) at none:1
Stacktrace:
 [1] (::ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing})(::Float64, ::DiffEqBase.NullParameters, ::Vararg{Any,N} where N) at /Users/kadowakimizuto/.julia/packages/DiffEqBase/pqp0B/src/diffeqfunction.jl:209
 [2] initialize!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},false,Float64,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},ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem},CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},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,DiffEqDiffTools.TimeDerivativeWrapper{ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing・・・文字数で割愛
 [3] initialize!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},false,Float64,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},ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem},CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},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,DiffEqDiffTools.TimeDerivativeWrapper{ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},DiffEqDiffTools.UDerivativeWrapper{ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},・・・文字数で割愛
 [4] #__init#333(::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Nothing, ::Bool, ::Bool, ::Bool, ::Bool, ::Nothing, ::Bool, ::Bool, ::Float64, ::Float64, ::Float64, ::Bool, ::Bool, ::Rational{Int64}, ::Nothing, ::Nothing, ::Rational{Int64}, ::Int64, ::Int64, ::Int64, ::Rational{Int64}, ::Bool, ::Int64, ::Nothing, ::Nothing, ::Int64, ::typeof(DiffEqBase.ODE_DEFAULT_NORM), ::typeof(LinearAlgebra.opnorm), ::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), ::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Int64, ::String, ::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), ::Nothing, ::Bool, ::Bool, ::Bool, ::Base.Iterators.Pairs{Symbol,Bool,Tuple{Symbol},NamedTuple{(:default_set,),Tuple{Bool}}}, ::typeof(DiffEqBase.__init), ::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Any,1}, ::Type{Val{true}}) at /Users/kadowakimizuto/.julia/packages/OrdinaryDiffEq/dfPRv/src/solve.jl:353
 [5] (::getfield(DiffEqBase, Symbol("#kw##__init")))(::NamedTuple{(:default_set,),Tuple{Bool}}, ::typeof(DiffEqBase.__init), ::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Any,1}, ::Type{Val{true}}) at ./none:0 (repeats 4 times)
 [6] #__solve#332(::Base.Iterators.Pairs{Symbol,Bool,Tuple{Symbol},NamedTuple{(:default_set,),Tuple{Bool}}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at /Users/kadowakimizuto/.julia/packages/OrdinaryDiffEq/dfPRv/src/solve.jl:4
 [7] (::getfield(DiffEqBase, Symbol("#kw##__solve")))(::NamedTuple{(:default_set,),Tuple{Bool}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at ./none:0
 [8] #__solve#2(::Bool, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Nothing) at /Users/kadowakimizuto/.julia/packages/DifferentialEquations/4jSpr/src/default_solve.jl:15
 [9] #solve#386 at ./none:0 [inlined]
 [10] solve(::ODEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters,ODEFunction{false,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}) at /Users/kadowakimizuto/.julia/packages/DiffEqBase/pqp0B/src/solve.jl:27
 [11] top-level scope at none:0

該当のソースコード

Julia
1using DifferentialEquations
2using Plots;gr()
3
4#人口問題に関する数理モデルを実行していく
5
6#微分方程式の定義
7f(y , t) = 0.3134 * y *(1 - y//(1.97*10^8))
8
9#初期値
10y0 = 3.9 * 10^6
11
12#時間間隔
13tspan = (0.0 , 10.0)
14
15#解いていく
16prob = ODEProblem(f , y0 , tspan)
17sol = solve(prob) ← ここでエラーになって上記の通
18plot(sol)

試したこと

なし

補足情報（FW/ツールのバージョンなど）

なし

coco_bauer

2019/09/10 08:03

『f(y , t) = 0.3134 * y *(1 - y//(1.97*10^8))』という微分方程式は、解けるのですか？「#人口問題に関する数理モデルを実行していく」とのコメントがありますが、『f(y , t) = 0.3134 * y *(1 - y//(1.97*10^8))』で数理モデルが表されているのですか？

行動規範の内容に同意します

回答1件

Julia のパッケージ DifferentialEquations の ODEProblem に渡す関数 f は、f(u, p, t) の形（p はパラメータなど）でなければいけません。
y//(1.97*10^8) は意味をなしていません。 // は有理数の計算のために使う演算子なので、変数 y と浮動小数点数 1.97*10^8 との演算は意味をなしてません。割り算には / を使いましょう。

julia
1using OrdinaryDiffEq
2using Plots; gr()
3
4#人口問題に関する数理モデルを実行していく
5
6#微分方程式の定義
7f(y, p, t) = 0.3134 * y * (1 - y / (1.97 * 10^8))
8
9#初期値
10y0 = 3.9 * 10^6
11
12#時間間隔
13tspan = (0.0, 10.0)
14
15#解いていく
16prob = ODEProblem(f, y0, tspan)
17sol = solve(prob)
18
19# retcode: Success
20# Interpolation: Automatic order switching interpolation
21# t: 9-element Array{Float64,1}:
22#   0.0
23#   0.12662428091680872
24#   0.7303457885946751
25#   1.7234344487967639
26#   2.907960396545146
27#   4.394365973752784
28#   6.13536084362757
29#   8.175248017875582
30#  10.0
31# u: 9-element Array{Float64,1}:
32#  3.9e6
33#  4.0546302666815394e6
34#  4.878256997996743e6
35#  6.599682298834936e6
36#  9.424427336760268e6
37#  1.4601936493607435e7
38#  2.3912221318911202e7
39#  4.087601240335912e7
40#  6.242186408738111e7
41
42plot(sol)
43