Error solving nonlinear boundary value problem / worked in a previous version of Julia 111 and Approxfun

[ChrisNabold]

I try to solve the following nonlinear Differential Equation/Boundary Value Problem: y'''' + 4.0*y'''/x = 0 with the following boundary conditions y(0) = y'(0) = 0 y''(1)=0 y'''(1)=1

in a previous version the following solution worked: using ApproxFun x = Fun(identity,0..5) u0 = 0.0x N = u->[u(0), u'(0), u''(1), u'''(1)-1, u''''+4*u^3/x] u = newton(N,u0)
Warning: Maximum numer of iterations 15 reached, with approximate accuracy of 1.439e-13

the results were ok

if I try to solve the same problem with the latest version I rceive the following error messages: ERROR: AssertionError: abs(first(g)) < tol Stacktrace:

if I change the statement N = u-> (because of singularity at x=0) to N = u->[u(0), u'(0), u''(1), u'''(1)-1, if x<1e-4 u''''+12*y'y^2 else u''''+4u^3/x end] u = newton(N,u0) I receive the same error message ERROR: AssertionError: abs(first(g)) < tol Stacktrace:

Can anybody help me

[dlfivefifty]

Please include stack traces when you post an issue

[ChrisNabold]

Dear Stephan,

Please find the requested stack trace:

Tank you for your help

Best regards

Chris

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julia> using ApproxFun

 

julia> println("\nResult using ApproxFun")

 

Result using ApproxFun

 

julia> x = Fun(identity,0..5)

Fun(Chebyshev(0..5),[2.5, 2.5])

 

julia> u0=0.0x

Fun(Chebyshev(0..5),[0.0, 0.0])

 

julia> N=u->[u(0),u'(0),u''(1),u'''(1)-1,u''''+4*u^3/x];

 

julia> u=newton(N,u0)

ERROR: AssertionError: abs(first(g)) < tol

Stacktrace:

  [1] coefficients(f::Vector{Float64}, sp1::JacobiWeight{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, IntervalSets.ClosedInterval{Int64}, Float64, Int64}, sp2::JacobiWeight{Chebyshev{Interval

Sets.ClosedInterval{Int64}, Float64}, IntervalSets.ClosedInterval{Int64}, Float64, Int64})

    @ ApproxFunSingularities C:\Users\Chris\.julia\packages\ApproxFunSingularities\abp7k\src\JacobiWeightChebyshev.jl:16

  [2] coefficients

    @ C:\Users\Chris\.julia\packages\ApproxFunSingularities\abp7k\src\JacobiWeight.jl:106 [inlined]

  [3] coefficients(f::Fun{JacobiWeight{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, IntervalSets.ClosedInterval{Int64}, Float64, Int64}, Float64, Vector{Float64}}, msp::Chebyshev{IntervalSets

.ClosedInterval{Int64}, Float64})

    @ ApproxFunBase C:\Users\Chris\.julia\packages\ApproxFunBase\Gra7W\src\Fun.jl:49

  [4] *(A::ApproxFunBase.ConstantTimesOperator{TimesOperator{Float64, Tuple{Int64, Int64}}, Float64}, b::Function)

    @ ApproxFunBase C:\Users\Chris\.julia\packages\ApproxFunBase\Gra7W\src\Operators\general\algebra.jl:611

  [5] /(B::ApproxFunBase.ConstantTimesOperator{TimesOperator{Float64, Tuple{Int64, Int64}}, Float64}, c::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}})

    @ ApproxFunBase C:\Users\Chris\.julia\packages\ApproxFunBase\Gra7W\src\Operators\general\algebra.jl:581

  [6] /(a::ApproxFun.DualFun{Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}, ApproxFunBase.ConstantTimesOperator{TimesOperator{Float64, Tuple{Int64, Int64}}, Float

64}}, b::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}})

    @ ApproxFun C:\Users\Chris\.julia\packages\ApproxFun\GOMNa\src\Extras\autodifferentiation.jl:54

  [7] (::var"#1#2")(u::ApproxFun.DualFun{Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}, ConstantOperator{Float64, Chebyshev{IntervalSets.ClosedInterval{Int64}, Fl

oat64}}})

    @ Main .\REPL[5]:1

  [8] newton(N::var"#1#2", u0::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}; maxiterations::Int64, tolerance::Float64)

    @ ApproxFun C:\Users\Chris\.julia\packages\ApproxFun\GOMNa\src\Extras\autodifferentiation.jl:98

  [9] newton(N::Function, u0::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}})

    @ ApproxFun C:\Users\Chris\.julia\packages\ApproxFun\GOMNa\src\Extras\autodifferentiation.jl:95

[10] top-level scope

    @ REPL[6]:1

[dlfivefifty]

The divide by x is probably an issue. Try multiplying through