ERROR: AssertionError: abs(last(g)) < tol when solving BVP ODE

[marcelosena]

Hi, I am trying to solve a two-point bvp with ApproxFun but receive the following error: ERROR: AssertionError: abs(last(g)) < tol I had a hard time searching what this error is supposed to mean (is it in the documentation somewhere?), but should I interpret it as an error on my end (not properly specifying the problem)? Or is it something else? Thanks.

[dlfivefifty]

Please post a MWE

[marcelosena]

Here, sorry:

using ApproxFun

r = 0.06 
δ = 0.1007
μ = 0.18
σ = 0.09
θ = 1.5
λ = 0.01
ℓ = 0.9
γ = 0.06
ϕ = 0.01

x = Fun()
u₀ = 1*x # initial guess
N = u->[u(0.19)-0.19;u(0) - 0; 0.5*σ^2*u'' + (x*δ + 1/(2*θ) + x/θ + x^2/(2*θ) + x*(r-λ) + μ )*u' + (-δ - 1/θ - x/θ - r)*u + u^2/(2*θ*u') ]
u = newton(N,u₀)

Updated guess and boundary conditions, I believe these to be more proper, although still have the same error.

[dlfivefifty]

Can you please include the error message when running the code

[marcelosena]

Here is the full output in REPL when running the code:

┌ Warning: Maximum length 1000000 reached.
└ @ ApproxFunBase C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Caching\matrix.jl:124
ERROR: AssertionError: abs(last(g)) < tol
Stacktrace:
 [1] coefficients(::Array{Float64,1}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Int64}) at C:\Users\Marcelo\.julia\packages\ApproxFunSingularities\MaPTr\src\JacobiWeightChebyshev.jl:20
 [2] coefficients at C:\Users\Marcelo\.julia\packages\ApproxFunSingularities\MaPTr\src\JacobiWeight.jl:106 [inlined]
 [3] coefficients(::Array{Float64,1}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64}, ::Chebyshev{ChebyshevInterval{Float64},Float64}, ::JacobiWeight{Ultraspherical{Int64,ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Int64}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Space.jl:312
 [4] defaultcoefficients(::Array{Float64,1}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64}, ::JacobiWeight{Ultraspherical{Int64,ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Int64}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Space.jl:341
 [5] coefficients(::Array{Float64,1}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64}, ::JacobiWeight{Ultraspherical{Int64,ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Int64}) at C:\Users\Marcelo\.julia\packages\ApproxFunSingularities\MaPTr\src\JacobiWeight.jl:93
 [6] coefficients(::Array{Float64,1}, ::JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64}, ::Ultraspherical{Int64,ChebyshevInterval{Float64},Float64}) at C:\Users\Marcelo\.julia\packages\ApproxFunSingularities\MaPTr\src\JacobiWeight.jl:106
 [7] coefficients at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Fun.jl:49 [inlined]
 [8] (::Base.var"#3#4"{typeof(coefficients)})(::Tuple{Fun{JacobiWeight{Chebyshev{ChebyshevInterval{Float64},Float64},ChebyshevInterval{Float64},Float64,Float64},Float64,Array{Float64,1}},Ultraspherical{Int64,ChebyshevInterval{Float64},Float64}}) at .\generator.jl:36
 [9] iterate at .\generator.jl:47 [inlined]
 [10] collect_to!(::Array{Array{Float64,1},1}, ::Base.Generator{Base.Iterators.Zip{Tuple{Array{Fun{S,Float64,Array{Float64,1}} where S,1},ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64}}},Base.var"#3#4"{typeof(coefficients)}}, ::Int64, ::Tuple{Int64,Int64}) at .\array.jl:710
 [11] collect_to_with_first!(::Array{Array{Float64,1},1}, ::Array{Float64,1}, ::Base.Generator{Base.Iterators.Zip{Tuple{Array{Fun{S,Float64,Array{Float64,1}} where S,1},ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64}}},Base.var"#3#4"{typeof(coefficients)}}, ::Tuple{Int64,Int64}) at .\array.jl:689
 [12] collect(::Base.Generator{Base.Iterators.Zip{Tuple{Array{Fun{S,Float64,Array{Float64,1}} where S,1},ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64}}},Base.var"#3#4"{typeof(coefficients)}}) at .\array.jl:670
 [13] map at .\abstractarray.jl:2154 [inlined]
 [14] coefficients(::Array{Fun{S,Float64,Array{Float64,1}} where S,1}, ::ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Spaces\ArraySpace.jl:208
 [15] coefficients(::Array{Any,1}, ::ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Spaces\ArraySpace.jl:211
 [16] \(::ApproxFunBase.InterlaceOperator{Float64,1,Chebyshev{ChebyshevInterval{Float64},Float64},ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64},ApproxFunBase.CachedIterator{Tuple{Int64,Int64},ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64,1,Tuple{InfiniteArrays.OneToInf{Int64}}}}}},ApproxFunBase.CachedIterator{Tuple{Int64,Int64},ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SArray{Tuple{1},Int64,1,1},StaticArrays.SArray{Tuple{1},Int64,1,1},FillArrays.Ones{Int64,1,Tuple{InfiniteArrays.OneToInf{Int64}}}}}},Tuple{InfiniteArrays.SignedInfinity,InfiniteArrays.Infinity}}, ::Array{Any,1}; kwds::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Operators\ldiv.jl:11
 [17] \(::ApproxFunBase.InterlaceOperator{Float64,1,Chebyshev{ChebyshevInterval{Float64},Float64},ApproxFunBase.ArraySpace{Space{D,Float64} where D,1,DomainSets.Point{Float64},Float64},ApproxFunBase.CachedIterator{Tuple{Int64,Int64},ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64,1,Tuple{InfiniteArrays.OneToInf{Int64}}}}}},ApproxFunBase.CachedIterator{Tuple{Int64,Int64},ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SArray{Tuple{1},Int64,1,1},StaticArrays.SArray{Tuple{1},Int64,1,1},FillArrays.Ones{Int64,1,Tuple{InfiniteArrays.OneToInf{Int64}}}}}},Tuple{InfiniteArrays.SignedInfinity,InfiniteArrays.Infinity}}, ::Array{Any,1}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Operators\ldiv.jl:4
 [18] \(::Array{Operator{Float64},1}, ::Array{Any,1}; kwds::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Operators\ldiv.jl:52
 [19] \(::Array{Operator{Float64},1}, ::Array{Any,1}) at C:\Users\Marcelo\.julia\packages\ApproxFunBase\Jv4NR\src\Operators\ldiv.jl:52
 [20] newton(::var"#138#139", ::Fun{Chebyshev{ChebyshevInterval{Float64},Float64},Float64,Array{Float64,1}}; maxiterations::Int64, tolerance::Float64) at C:\Users\Marcelo\.julia\packages\ApproxFun\hDuHj\src\Extras\autodifferentiation.jl:101
 [21] newton(::Function, ::Fun{Chebyshev{ChebyshevInterval{Float64},Float64},Float64,Array{Float64,1}}) at C:\Users\Marcelo\.julia\packages\ApproxFun\hDuHj\src\Extras\autodifferentiation.jl:95
 [22] top-level scope at REPL[393]:1

[dlfivefifty]

The Warning: Maximum length 1000000 reached means something has failed to converge. Likely your initial guess is not accurate enough and the Newton solver has spun out of control.

[dlfivefifty]

May I suggest a homotopy method for producing the initial guess? That is, choose "nicer" parameters that converge and use that as initial guesses as you approach the desired parameters.