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docs/src/basics/error_control.md

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When comes to solving ill-conditioned BVP, for example the singular perturbation problem where the small parameters become extremely small leading to the layers phonemona, the error control adaptivity becomes even more critical, because the minor perturbations can lead to large deviation in the solution. In such cases, adaptivity automatically figure out where to use refined mesh and where to use coarse mesh to achieve the balance of computational efficiency and accuracy.
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BoundaryValuDiffEq.jl support error control adaptivity for collocation methods, and the adaptivity is default as defect control adaptivity when using adaptive collocation solvers:
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BoundaryValueDiffEq.jl support error control adaptivity for collocation methods, and the adaptivity is default as defect control adaptivity when using adaptive collocation solvers:
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```julia
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sol = solve(prob, MIRK4(), dt = 0.01, adaptive = true)

docs/src/basics/solve.md

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- `controller`: Error controller for collocation methods, default as `DefectControl()`, more controller options in [Error Control Adaptivity](@ref error_control).
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- `defect_threshold`: Monitor of the size of defect norm. Defaults to `0.1`.
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- `odesolve_kwargs`: OrdinaryDiffEq.jl solvers kwargs for passing to ODE solving in shooting methods. For more information, see the documentation for OrdinaryDiffEq: [Common Solver Options](https://docs.sciml.ai/DiffEqDocs/latest/basics/common_solver_opts/).
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- `nlsolve_kwargs`: NonlinearSolve.jl solvers kwargs for passing to nonlinear solving in collocation methods and shooting methods. For more information, see the documentation for NonlinearSolve: [Commom Solver Options](https://docs.sciml.ai/NonlinearSolve/stable/basics/solve/). The default internal nonlinear solver is [customized polyalgorithm](https://github.com/SciML/BoundaryValueDiffEq.jl/blob/master/lib/BoundaryValueDiffEqCore/src/default_nlsolve.jl) and the default absolute tolerance of nonlinear solving in collocation and shooting methods is `1e-6`.
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- `optimize_kwargs`: Optimization.jl solvers kwargs for passing to optimization problem solving in collocation methods and shooting methods. For more information, see the documentation for Optimization: [Commom Solver Options](https://docs.sciml.ai/Optimization/stable/API/solve/). The internal optimization solver should be specified and the default absolute tolerance of optimization problem solving in collocation and shooting methods is `1e-6`.
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- `nlsolve_kwargs`: NonlinearSolve.jl solvers kwargs for passing to nonlinear solving in collocation methods and shooting methods. For more information, see the documentation for NonlinearSolve: [Common Solver Options](https://docs.sciml.ai/NonlinearSolve/stable/basics/solve/). The default internal nonlinear solver is [customized polyalgorithm](https://github.com/SciML/BoundaryValueDiffEq.jl/blob/master/lib/BoundaryValueDiffEqCore/src/default_nlsolve.jl) and the default absolute tolerance of nonlinear solving in collocation and shooting methods is `1e-6`.
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- `optimize_kwargs`: Optimization.jl solvers kwargs for passing to optimization problem solving in collocation methods and shooting methods. For more information, see the documentation for Optimization: [Common Solver Options](https://docs.sciml.ai/Optimization/stable/API/solve/). The internal optimization solver should be specified and the default absolute tolerance of optimization problem solving in collocation and shooting methods is `1e-6`.
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- `verbose`: Toggles whether warnings are thrown when the solver exits early. Defaults to `true`.
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- `ensemblealg`: Whether `MultipleShooting` uses multithreading, default as `EnsembleThreads()`. For more information, see the documentation for OrdinaryDiffEq: [EnsembleAlgorithms](https://docs.sciml.ai/DiffEqDocs/latest/features/ensemble/#EnsembleAlgorithms).

docs/src/solvers/mirk.md

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# [BoundaryValueDiffEqMIRK](@id mirk)
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Monotonic Implicit Runge Kutta(MIRK) Methods. To only use the MIRK methods form BoundaryVaueDiffEq.jl, you need to install them use the Julia package manager:
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Monotonic Implicit Runge Kutta(MIRK) Methods. To only use the MIRK methods form BoundaryValueDiffEq.jl, you need to install them use the Julia package manager:
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```julia
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using Pkg

docs/src/solvers/mirkn.md

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# [BoundaryValueDiffEqMIRKN](@id mirkn)
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Monotonic Implicit Runge Kutta Nyström(MIRKN) Methods. To only use the MIRKN methods form BoundaryVaueDiffEq.jl, you need to install them use the Julia package manager:
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Monotonic Implicit Runge Kutta Nyström(MIRKN) Methods. To only use the MIRKN methods form BoundaryValueDiffEq.jl, you need to install them use the Julia package manager:
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```julia
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using Pkg

docs/src/solvers/shooting.md

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# [BoundaryValueDiffEqShooting](@id shooting)
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Single shooting method and multiple shooting method. To only use the Shooting methods form BoundaryVaueDiffEq.jl, you need to install them use the Julia package manager:
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Single shooting method and multiple shooting method. To only use the Shooting methods form BoundaryValueDiffEq.jl, you need to install them use the Julia package manager:
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```julia
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using Pkg

docs/src/tutorials/solve_nlls_bvp.md

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plot(sol)
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```
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Since this BVP imposes constraints only at the two endpoints, we can use `TwoPointBVProlem` to handle such cases.
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Since this BVP imposes constraints only at the two endpoints, we can use `TwoPointBVProblem` to handle such cases.
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```@example nlls_overdetermined
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function f!(du, u, p, t)

lib/BoundaryValueDiffEqCore/src/calc_errors.jl

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end
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"""
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GlobalErrorControl(; method = HOErorControl())
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GlobalErrorControl(; method = HOErrorControl())
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Global error controller, use high order global error estimation method `HOErrorControl` as default.
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"""

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