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README.md

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# MethodOfLines.jl
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Provides automatic discretization of symbolic PDE systems as defined with ModelingToolkit.jl
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Provides automatic discretization of symbolic PDE systems as defined with ModelingToolkit.jl.
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Feature requests and issues welcome.
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## Usage:
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```
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grid_align = your grid type choice>)
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prob = discretize(pdesys, discretization)
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```
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Where dxs is a vector of pairs of parameters to the grid step in this dimension, i.e. `[x=>0.2, y=>0.1]`
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Where `dxs` is a vector of pairs of parameters to the grid step in this dimension, i.e. `[x=>0.2, y=>0.1]`
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Note that the second argument to `MOLFiniteDifference` is optional, all parameters can be discretized if all boundary conditions are specified
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Currently supported grid types: `center_align` and `edge_align`
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center_align: naive grid, starting from lower boundary, ending on upper boundary with step of dx
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`center_align`: naive grid, starting from lower boundary, ending on upper boundary with step of `dx`
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edge_align: offset grid, set halfway between the points that would be generated with center_align, with extra points at either end that are above and below the supremum and infimum by dx/2.
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`edge_align`: offset grid, set halfway between the points that would be generated with center_align, with extra points at either end that are above and below the supremum and infimum by `dx/2`.
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This provides higher accuracy with neumann/robin boundary conditions.
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Currently boundary conditions defined in terms of derivatives at the boundary are unsupported above 1 discretized dimension. Periodic conditions are also unsupported.
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## Coming soon:
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- Arbitrary approximation order
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- Above mentioned unsupported boundary conditions supported
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- Staggered grids
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- More types of domain
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## Full Example:
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```

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