@@ -10,7 +10,7 @@ equation (BRUSS) using NonlinearSolve.jl.
1010## Definition of the Brusselator Equation
1111
1212!!! note
13-
13+
1414 Feel free to skip this section: it simply defines the example problem.
1515
1616The Brusselator PDE is defined as follows:
@@ -117,11 +117,11 @@ However, if you know the sparsity of your problem, then you can pass a different
117117type. For example, a ` SparseMatrixCSC ` will give a sparse matrix. Other sparse matrix types
118118include:
119119
120- - Bidiagonal
121- - Tridiagonal
122- - SymTridiagonal
123- - BandedMatrix ([ BandedMatrices.jl] ( https://github.com/JuliaLinearAlgebra/BandedMatrices.jl ) )
124- - BlockBandedMatrix ([ BlockBandedMatrices.jl] ( https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl ) )
120+ - Bidiagonal
121+ - Tridiagonal
122+ - SymTridiagonal
123+ - BandedMatrix ([ BandedMatrices.jl] ( https://github.com/JuliaLinearAlgebra/BandedMatrices.jl ) )
124+ - BlockBandedMatrix ([ BlockBandedMatrices.jl] ( https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl ) )
125125
126126## Approximate Sparsity Detection & Sparse Jacobians
127127
@@ -167,7 +167,7 @@ and `u` and call `jacobian_sparsity` on our function with the example arguments,
167167kick out a sparse matrix with our pattern, that we can turn into our ` jac_prototype ` .
168168
169169!!! tip
170-
170+
171171 Alternatively you can use the ` SparseConnectivityTracer.jl ` package to automatically
172172 generate a sparse Jacobian.
173173
@@ -224,7 +224,7 @@ choices, see the
224224` linsolve ` choices are any valid [ LinearSolve.jl] ( https://linearsolve.sciml.ai/dev/ ) solver.
225225
226226!!! note
227-
227+
228228 Switching to a Krylov linear solver will automatically change the nonlinear problem
229229 solver into Jacobian-free mode, dramatically reducing the memory required. This can be
230230 overridden by adding ` concrete_jac=true ` to the algorithm.
@@ -330,7 +330,7 @@ prob_brusselator_2d_exact_tracer = NonlinearProblem(
330330 u0, p; abstol = 1e-10, reltol = 1e-10)
331331prob_brusselator_2d_approx_di = NonlinearProblem(
332332 NonlinearFunction(brusselator_2d_loop;
333- sparsity = DenseSparsityDetector(AutoForwardDiff(); atol= 1e-4)),
333+ sparsity = DenseSparsityDetector(AutoForwardDiff(); atol = 1e-4)),
334334 u0, p; abstol = 1e-10, reltol = 1e-10)
335335
336336@btime solve(prob_brusselator_2d_exact_symbolics, NewtonRaphson());
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