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5 changes: 2 additions & 3 deletions README.md
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# MethodOfLines.jl

[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](http://methodoflines.sciml.ai/stable/)
[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/dev/modules/MethodOfLines/)
[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/MethodOfLines/stable/)

[![codecov](https://codecov.io/gh/SciML/MethodOfLines.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/MethodOfLines.jl)
[![Build Status](https://github.com/SciML/MethodOfLines.jl/workflows/CI/badge.svg)](https://github.com/SciML/MethodOfLines.jl/actions?query=workflow%3ACI)
Expand All @@ -15,7 +14,7 @@ of symbolically-defined PDEs in N dimensions.

It uses symbolic expressions for systems of partial differential equations as defined with `ModelingToolkit.jl`, and `Interval` from `DomainSets.jl` to define the space(time) over which the simulation runs.

This project is under active development, therefore the interface is subject to change. The [docs](http://methodoflines.sciml.ai/dev/) will be updated to reflect any changes, please check back for current usage information.
This project is under active development, therefore the interface is subject to change. The [docs](https://docs.sciml.ai/MethodOfLines/dev/) will be updated to reflect any changes, please check back for current usage information.

Note that this package does not currently scale well to high resolution (high point count) problems, though there are changes in the works to remedy this.

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2 changes: 1 addition & 1 deletion docs/make.jl
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Expand Up @@ -20,7 +20,7 @@ makedocs(sitename = "MethodOfLines.jl",
modules = [MethodOfLines],
format = Documenter.HTML(analytics = "UA-90474609-3",
assets = ["assets/favicon.ico"],
canonical = "https://methodoflines.sciml.ai/stable/"),
canonical = "https://docs.sciml.ai/MethodOfLines/stable/"),
pages = pages)

deploydocs(repo = "github.com/SciML/MethodOfLines.jl"; push_preview = true)
2 changes: 1 addition & 1 deletion docs/src/MOLFiniteDifference.md
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Expand Up @@ -49,4 +49,4 @@ Currently supported grid types: `center_align` and `edge_align`. Edge align will

`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`. This improves accuracy for Neumann BCs.

Any unrecognized keyword arguments will be passed to the `ODEProblem` constructor, see [its documentation](https://mtk.sciml.ai/stable/systems/ODESystem/#Standard-Problem-Constructors) for available options.
Any unrecognized keyword arguments will be passed to the `ODEProblem` constructor, see [its documentation](https://docs.sciml.ai/ModelingToolkit/stable/systems/ODESystem/#Standard-Problem-Constructors) for available options.
2 changes: 1 addition & 1 deletion docs/src/advection_schemes.md
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Expand Up @@ -15,7 +15,7 @@ A more stable scheme, 5th order accurate, which is a weighted sum of several dif

`epsilon`is a quantity used to prevent vanishing denominators in the scheme, defaults to `1e-6`. Problems with a lower magnitude solution will benefit from a smaller value.

Problems which require this scheme may also benefit from a [Strong-Stability-Preserving (SSP) solver](https://diffeq.sciml.ai/stable/solvers/ode_solve/#Explicit-Strong-Stability-Preserving-Runge-Kutta-Methods-for-Hyperbolic-PDEs-(Conservation-Laws)).
Problems which require this scheme may also benefit from a [Strong-Stability-Preserving (SSP) solver](https://docs.sciml.ai/DiffEqDocs/stable/solvers/ode_solve/#Explicit-Strong-Stability-Preserving-Runge-Kutta-Methods-for-Hyperbolic-PDEs-(Conservation-Laws)).

Problems with first order derivatives which multiply one another will need to use this scheme over the upwind scheme.

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2 changes: 1 addition & 1 deletion docs/src/index.md
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Expand Up @@ -18,7 +18,7 @@ Allowable terms in the system include, but are not limited to
- Reaction
- Nonlinear Diffusion
- Spherical laplacian
- Any Julia function of the symbolic parameters/dependant variables and other parameters in the environment that's defined on the whole domain. Note that more complicated functions may require registration with `@register`, see the [ModelingToolkit.jl docs](https://mtk.sciml.ai/stable/basics/Validation/#User-Defined-Registered-Functions-and-Types).
- Any Julia function of the symbolic parameters/dependant variables and other parameters in the environment that's defined on the whole domain. Note that more complicated functions may require registration with `@register`, see the [ModelingToolkit.jl docs](https://docs.sciml.ai/ModelingToolkit/stable/basics/Validation/#User-Defined-Registered-Functions-and-Types).

Boundary conditions include, but are not limited to:
- Dirichlet
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4 changes: 2 additions & 2 deletions docs/src/tutorials/brusselator.md
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Expand Up @@ -42,7 +42,7 @@ on a timespan of ``t \in [0,11.5]``.

## Solving with MethodOfLines

With `ModelingToolkit.jl`, we first symbolicaly define the system, see also the docs for [`PDESystem`](https://mtk.sciml.ai/stable/systems/PDESystem/):
With `ModelingToolkit.jl`, we first symbolicaly define the system, see also the docs for [`PDESystem`](https://docs.sciml.ai/ModelingToolkit/stable/systems/PDESystem/):

```julia
using ModelingToolkit, MethodOfLines, OrdinaryDiffEq, DomainSets
Expand Down Expand Up @@ -112,7 +112,7 @@ println("Discretization:")
```

## Solving the problem
Now your problem can be solved with an appropriate ODE solver, or Nonlinear solver if you have not supplied a time dimension in the `MOLFiniteDifference` constructor. Include these solvers with `using OrdinaryDiffEq` or `using NonlinearSolve`, then call `sol = solve(prob, AppropriateSolver())` or `sol = NonlinearSolve.solve(prob, AppropriateSolver())`. For more information on the available solvers, see the docs for [`DifferentialEquations.jl`](https://diffeq.sciml.ai/stable/solvers/ode_solve/), [`NonlinearSolve.jl`](http://nonlinearsolve.sciml.ai/dev/solvers/NonlinearSystemSolvers/) and [SteadyStateDiffEq.jl](https://diffeq.sciml.ai/stable/solvers/steady_state_solve/#SteadyStateDiffEq.jl). `Tsit5()` is a good first choice of solver for many problems.
Now your problem can be solved with an appropriate ODE solver, or Nonlinear solver if you have not supplied a time dimension in the `MOLFiniteDifference` constructor. Include these solvers with `using OrdinaryDiffEq` or `using NonlinearSolve`, then call `sol = solve(prob, AppropriateSolver())` or `sol = NonlinearSolve.solve(prob, AppropriateSolver())`. For more information on the available solvers, see the docs for [`DifferentialEquations.jl`](https://docs.sciml.ai/DiffEqDocs/stable/solvers/ode_solve/), [`NonlinearSolve.jl`](http://docs.sciml.ai/NonlinearSolve/stable/solvers/NonlinearSystemSolvers/) and [SteadyStateDiffEq.jl](https://docs.sciml.ai/DiffEqDocs/stable/solvers/steady_state_solve/#SteadyStateDiffEq.jl). `Tsit5()` is a good first choice of solver for many problems.

```julia
println("Solve:")
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2 changes: 1 addition & 1 deletion docs/src/tutorials/params.md
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Expand Up @@ -48,7 +48,7 @@ gif(anim, "plot.gif",fps=30)

## Remake with different parameter values

The system does not need to be re-discretized every time we want to plot with different parameters, the system can be remade with new parameters with `remake`. See the `ModelingToolkit.jl` [docs](https://mtk.sciml.ai/stable/tutorials/ode_modeling/#Algebraic-relations-and-structural-simplification) for more ways to manipulate a `prob` post discretization.
The system does not need to be re-discretized every time we want to plot with different parameters, the system can be remade with new parameters with `remake`. See the `ModelingToolkit.jl` [docs](https://docs.sciml.ai/ModelingToolkit/stable/tutorials/ode_modeling/#Algebraic-relations-and-structural-simplification) for more ways to manipulate a `prob` post discretization.

```@example params2
using ModelingToolkit, MethodOfLines, OrdinaryDiffEq, DomainSets
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2 changes: 1 addition & 1 deletion docs/src/tutorials/sispde.md
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Expand Up @@ -95,7 +95,7 @@ display(p)

Change the elliptic problem to steady state problem of reaction diffusion equation.

See more solvers in [Steady State Solvers · DifferentialEquations.jl](https://diffeq.sciml.ai/stable/solvers/steady_state_solve/)
See more solvers in [Steady State Solvers · DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/solvers/steady_state_solve/)

```@example sispde
steadystateprob = SteadyStateProblem(prob)
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