# BoundaryValueDiffEq: How to restart to exploit initial guess?

**URL:** <https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552>\
**Category:** Specific Domains\
**Tags:** question\
**Created:** [February 4, 2025, 7:28pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552 "2025-02-04T19:28:10Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![Domenico\_Lahaye](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/domenico_lahaye/32/203728_2.png) [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Post date:** [February 4, 2025, 7:28pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/1 "2025-02-04T19:28:10Z")

</div>

My boundary value problem has a parameter that renders the problem easy or hard.

Is there a way to restart the solve function for the hard problem by specifying the solution of the easy problem as initial guess?

Below a MWE (solves Burgers equation by harmonic balancing. If nonlinscaling=0 (see below), problem reduces to linear Helmholtz equation)

```julia
# set source function 
src(x) = 1. 

# set right-hand side 
function rhs!(du, u, p, x)
    c, omd = p
    C = u[1]; A = u[2]; B = u[3]
    dC = du[1]; dA = du[2]; dB = du[3]
    nonlinscaling = 0.2
    du[1] = nonlinscaling*(A*dA+B*dB+C*dC)
    du[2] = omd/c*B + nonlinscaling*(A*dC+C*dA) 
    du[3] = -omd/c*A - src(x)/c + nonlinscaling*(B*dC+C*dB) 
end

# set boundary conditions 
function bc(residual, u, p, x)
    Cleft = 0; Aleft = 0; Bleft=0; 
    residual[1] = u[1][1] - Cleft
    residual[2] = u[1][2] - Aleft 
    residual[3] = u[1][3] - Bleft 
end

# set constants 
c = 0.2
omd = 2*pi
p = [c, omd]

# set domain size 
xspan = (0.,1.)

# set initial guess 
start = [0., 1., 1.]

# define and solve the problem 
bvp = BVProblem(rhs!, bc, start, xspan,p)
sol = solve(bvp, MIRK4(), dt = 0.005)

```

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<div class="post-metadata">

**Author:** ![ErikQQY](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erikqqy/32/23074_2.png) [@ErikQQY](https://discourse.julialang.org/u/ErikQQY)\
**Post date:** [February 5, 2025, 4:34pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/2 "2025-02-05T16:34:49Z")

</div>

BoundaryValueDifEq.jl does support using the solution from previous solving in the next solving, just pass the solution to the construction of BVProblem with `BVProblem(the!, bc, sol.u, xspan, p)` and call the solver on this new problem.

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<div class="post-metadata">

**Author:** ![Domenico\_Lahaye](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/domenico_lahaye/32/203728_2.png) [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Post date:** [February 5, 2025, 6:33pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/3 "2025-02-05T18:33:48Z")

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I run into a method error.

Is there any example on this?

Thx!

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<div class="post-metadata">

**Author:** ![ErikQQY](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erikqqy/32/23074_2.png) [@ErikQQY](https://discourse.julialang.org/u/ErikQQY)\
**Post date:** [February 5, 2025, 7:24pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/4 "2025-02-05T19:24:41Z")

</div>

Could you please share your error stacktrace?

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<div class="post-metadata">

**Author:** ![Domenico\_Lahaye](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/domenico_lahaye/32/203728_2.png) [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Post date:** [February 5, 2025, 7:31pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/5 "2025-02-05T19:31:57Z")

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Sure.

```julia
solrestart = sol;

nonlinscaling = 0.5 

# store parameter value in p
p = [c, omd, nonlinscaling]

# define and solve the problem 
bvp = BVProblem(rhs!, bc, solrestart.u, xspan,p)
sol = solve(bvp, MIRK4(), dt = 0.005)

```

results in

```julia
MethodError: no method matching zero(::Type{Vector{Float64}})
Closest candidates are:
  zero(::Union{Type{P}, P}) where P<:Dates.Period at /Applications/Julia-1.8.app/Contents/Resources/julia/share/julia/stdlib/v1.8/Dates/src/periods.jl:53
  zero(::G) where G<:Graphs.AbstractGraph at ~/.julia/packages/Graphs/FXxqo/src/interface.jl:346
  zero(::OffsetArrays.OffsetArray) at ~/.julia/packages/OffsetArrays/xdnHf/src/OffsetArrays.jl:407
  ...

Stacktrace:
 [1] zeros(#unused#::Type{Vector{Float64}}, dims::Tuple{Int64})
   @ Base ./array.jl:589
 [2] zeros(#unused#::Type{Vector{Float64}}, dims::Int64)
   @ Base ./array.jl:584
 [3] vector_alloc
   @ ~/.julia/packages/BoundaryValueDiffEq/xfc07/src/vector_auxiliary.jl:5 [inlined]
 [4] BoundaryValueDiffEq.BVPSystem(prob::BVProblem{Vector{Vector{Float64}}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(rhs!), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(bc), SciMLBase.StandardBVProblem, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, x::Vector{Float64}, order::Int64)
   @ BoundaryValueDiffEq ~/.julia/packages/BoundaryValueDiffEq/xfc07/src/collocation.jl:21
 [5] __solve(prob::BVProblem{Vector{Vector{Float64}}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(rhs!), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(bc), SciMLBase.StandardBVProblem, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, alg::MIRK4; dt::Float64, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ BoundaryValueDiffEq ~/.julia/packages/BoundaryValueDiffEq/xfc07/src/solve.jl:32
 [6] solve_call(_prob::BVProblem{Vector{Vector{Float64}}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(rhs!), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(bc), SciMLBase.StandardBVProblem, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, args::MIRK4; merge_callbacks::Bool, kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:dt,), Tuple{Float64}}})
   @ DiffEqBase ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:221
 [7] solve_up(prob::BVProblem{Vector{Vector{Float64}}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(rhs!), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(bc), SciMLBase.StandardBVProblem, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, sensealg::Nothing, u0::Vector{Vector{Float64}}, p::Vector{Float64}, args::MIRK4; kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:dt,), Tuple{Float64}}})
   @ DiffEqBase ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:254
 [8] solve(prob::BVProblem{Vector{Vector{Float64}}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(rhs!), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(bc), SciMLBase.StandardBVProblem, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, args::MIRK4; sensealg::Nothing, u0::Nothing, p::Nothing, kwargshandle::KeywordArgError, kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:dt,), Tuple{Float64}}})
   @ DiffEqBase ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:234
 [9] top-level scope
   @ In[13]:10

```

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<div class="post-metadata">

**Author:** ![apo383](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/apo383/32/11272_2.png) [@apo383](https://discourse.julialang.org/u/apo383)\
**Post date:** [February 5, 2025, 9:44pm UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/6 "2025-02-05T21:44:05Z")

</div>

What version are you using? Looking at the stack trace, `src/vector_auxiliary.jl` and `src/collocation.jl` don’t seem to be in current [BoundaryValueDiffEq.jl](https://github.com/SciML/BoundaryValueDiffEq.jl/). But searching outside the repo in GitHub, they are in forks dating back about 5-7 years.

You seem to be on Julia 1.8, and `BoundaryValueDiffEq.jl` has changed a lot since then. Can report the Pkg status `]st`?

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<div class="post-metadata">

**Author:** ![ErikQQY](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erikqqy/32/23074_2.png) [@ErikQQY](https://discourse.julialang.org/u/ErikQQY)\
**Post date:** [February 6, 2025, 3:49am UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/7 "2025-02-06T03:49:36Z")

</div>

You are using an old version of BoundaryValueDiffEq.jl, exploiting initial guess requires the latest version of BoundaryValueDiffEq.jl

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<div class="post-metadata">

**Author:** ![Domenico\_Lahaye](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/domenico_lahaye/32/203728_2.png) [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Post date:** [February 6, 2025, 7:46am UTC](https://discourse.julialang.org/t/boundaryvaluediffeq-how-to-restart-to-exploit-initial-guess/125552/8 "2025-02-06T07:46:36Z")

</div>

Switching to Julia 1.10 solved the issue.

You are heros! Many thx!