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* switch to OrdinaryDiffEqCore.jl
* bump compat of SciMLBase.j to v2.68
* bump version of SymbolicIndexingInterface.jl to v0.3.36
* drop support for FastBroadcast v0.3
* do not import OrdinaryDiffEq
* add missing compat bounds
* set compat bounds of stdlibs to 1
* use OrdinaryDiffEq.jl subpackages in tests
* use OrdinaryDiffEq.jl subpackages
* fix another using OrdinaryDiffEq
* use OrdinaryDiffEq.jl subpackages in docs
* add compat for OrdinaryDiffEqRosenbrock.jl in docs
* fix typo in docs
* fix step!
* use ADTypes.jl to fix deprecation warnings
* format
* apply new formatter version
* bump compat of FastBroadcast.jl to v0.3.1 (v0.3.0 is yanked)
* fix typo
* bump FastBroadcast to v0.3.4
* lower compat bound of OrdinaryDiffEqCore.jl to v1.6
* bump compat bound of Reexport.jl to v1.2.2
* lower compat bound of OrdinaryDiffEqRosenbrock.jl v1.3
* bump compat bound of MuladdMacro.jl to v0.2.4
* bump compat for StaticArrays.jl to v1.9.7
* bump compat for StaticArrays.jl to v1.9.7
* bump compat for FastBroadcast.jl v0.3.5
* fix get_tmp_cache
* fix solve!
* bump compat of LinearSolve.jl to v2.32
* also bump LinearSolve.jl to v2.32 in docs an test
* bump compat of Plots.jl to v1.25.11
* bump compat of OrdinaryDiffEqCore.jl to v1.15.1
* bump compat of OrdinaryDiffEqCore.jl to v1.16
* bump compat of OrdinaryDiffEqRosenbrock to v1.4
* bump compat of OrdinaryDiffEqSDIRK.jl to v1.2
To solve this PDS together with initial values ``u_1(0)=u_2(0)=2`` on the time domain ``(0,10)``, we first need to create a `PDSProblem`.
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```@example LotkaVolterra
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The following example shows how to implement the above SIR model with ``\beta=0.4, \gamma=0.04``, initial conditions ``S(0)=997, I(0)=3, R(0)=0`` and time domain ``(0, 100)`` using `ConservativePDSProblem` from [PositiveIntegrators.jl](https://github.com/SKopecz/PositiveIntegrators.jl).
and we consider the initial conditions ``N=8``, ``P=2``, ``Z=1`` and ``D=4``. The time domain of interest is ``t\in[0,10]``.
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and we consider the initial conditions ``N=8``, ``P=2``, ``Z=1`` and ``D=4``. The time domain of interest is ``t\in[0,10]``.
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The model can be represented as a conservative PDS with production terms
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```math
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## Solution of the production-destruction system
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-
Now we are ready to define a [`ConservativePDSProblem`](@ref) and to solve this problem with a method of [PositiveIntegrators.jl](https://github.com/SKopecz/PositiveIntegrators.jl) or [OrdinaryDiffEq.jl](https://docs.sciml.ai/OrdinaryDiffEq/stable/).
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Now we are ready to define a [`ConservativePDSProblem`](@ref) and to solve this problem with a method of [PositiveIntegrators.jl](https://github.com/SKopecz/PositiveIntegrators.jl) or [OrdinaryDiffEq.jl](https://docs.sciml.ai/OrdinaryDiffEq/stable/).
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As mentioned above, we will try different approaches to solve this PDS and compare their efficiency. These are
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1. an out-of-place implementation with standard (dynamic) matrices and vectors,
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