# BVProblem with solver RadauIIa5: a very simple MWE yields all-zero results (?)

**URL:** <https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510>\
**Category:** General Usage\
**Tags:** diffeq\
**Created:** [February 4, 2025, 12:11am UTC](https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510 "2025-02-04T00:11:52Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![P0p5](https://avatars.discourse-cdn.com/v4/letter/p/45deac/32.png) [@P0p5](https://discourse.julialang.org/u/P0p5)\
**Post date:** [February 4, 2025, 12:11am UTC](https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510/1 "2025-02-04T00:11:52Z")

</div>

When I run the very simple MWE posted below containing BVProblem which specifies solver RadauIIa5, it runs with a return code “Unstable”, and produces unexpected all-zero results.  
In view of the simplicity of this problem, I wonder what I might have done wrong.  
I would appreciate it if you could identify any mistake(s).

I would also appreciate the identification of any benchmark run in the Julia language with this solver, together with its numerical results. All the benchmarks in the online documentation seem to have used other languages.

Please also consider the question appearing as one of the comments in this MWE.  
thanks.

```julia-auto

# This example using BVProblem with solver RadauIIa5 is 
# an attempt to reproduce the analytic solution... 
# y(t) = t^2 + 10.

```

using BoundaryValueDiffEqFIRK

function f!(dy\_dt, y, par, t)

# It seems that t is provided as a vector.

# (A vector might have been expected only for an “orthogonal collocation method”.)

```
dy_dt = 2.0 .* t

[dy_dt] # These square brackets are not required, and don't seem to matter.

```

end

function initialGuess(t)

# And here, t again seems to be a vector

# The arguments of this function appear to be undocumented.

# We use the correct solution but without the constant, as the initial guess

```
[t .* t] # If these square brackets are absent ==> error msg! Why the difference?    

```

end

function bc!(resid, y, par, t) # Boundary conditions

# Here again t seems to be a vector.

```
resid[1] = abs(y[1,1] - 11.0)      

```

end

tspan = (1.0, 10.0)

bvp = BVProblem(f!, bc!, initialGuess , tspan, 0.0)

sol = solve(bvp, RadauIIa5(); dt = 0.1, abstol=1e-2, reltol=1e-2)

```julia-auto
Result below…

```

julia\> include(“../../../BVProblem,Example3.jl”)  
retcode: Unstable  
Interpolation: FIRK Order 9 Interpolation  
t: 2881-element Vector{Float64}:  
1.0  
1.003125  
1.00625  
1.009375  
1.0125  
1.015625  
1.0187499999999998  
1.0218749999999999  
1.025  
1.028125  
1.03125  
1.034375  
1.0375  
1.0406250000000001  
1.0437500000000002  
1.046875  
1.05  
1.053125  
1.05625  
1.059375  
1.0625  
1.065625  
1.06875  
1.0718750000000001  
1.0750000000000002  
⋮  
9.928125000000001  
9.93125  
9.934375  
9.9375  
9.940625  
9.94375  
9.946874999999999  
9.95  
9.953125  
9.956249999999999  
9.959374999999998  
9.962499999999999  
9.965625  
9.96875  
9.971875  
9.975  
9.978124999999999  
9.98125  
9.984375  
9.9875  
9.990625000000001  
9.99375  
9.996875  
10.0  
u: 2881-element Vector{Vector{Float64}}:  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
⋮  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]  
[0.0]

julia\>

```julia-auto
I get the same result with this modification:

```

function bc!(resid, sol, par, t) # Boundary conditions

# Here again t seems to be a vector.

```
resid[1] = abs(sol[1,1] - 11.0)      

```

end

```julia-auto
And this gives a syntax error (?) ...

```

# resid[2] = abs(sol1 - 110.0) # But this gives a syntax error (?)

```julia-auto

```

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<div class="post-metadata">

**Author:** ![P0p5](https://avatars.discourse-cdn.com/v4/letter/p/45deac/32.png) [@P0p5](https://discourse.julialang.org/u/P0p5)\
**Post date:** [February 4, 2025, 2:57am UTC](https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510/2 "2025-02-04T02:57:47Z")

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I don’t know how the comments got exploded. It looks like I quoted the pasted text correctly.

---

<div class="post-metadata">

**Author:** ![JM\_Beckers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jm_beckers/32/22482_2.png) [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)\
**Post date:** [February 4, 2025, 6:56am UTC](https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510/3 "2025-02-04T06:56:04Z")

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```julia
function f!(dy_dt, y, par, t)

dy_dt[1] = 2.0 .* t

end

```

---

<div class="post-metadata">

**Author:** ![P0p5](https://avatars.discourse-cdn.com/v4/letter/p/45deac/32.png) [@P0p5](https://discourse.julialang.org/u/P0p5)\
**Post date:** [February 4, 2025, 7:16am UTC](https://discourse.julialang.org/t/bvproblem-with-solver-radauiia5-a-very-simple-mwe-yields-all-zero-results/125510/4 "2025-02-04T07:16:20Z")

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Thank you! That worked.