chore: apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: avik-pal

docs/src/basics/sparsity_detection.md

@@ -34,7 +34,7 @@ If the `colorvec` is not provided, then it is computed on demand.
     row colorvec.
 
 !!! warning
-
+    
     Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
     the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
     use the `jac_prototype` argument.
@@ -58,7 +58,7 @@ sparsity detection algorithms.
 ## Case III: Sparse AD Type is being Used
 
 !!! warning
-
+    
     This is now deprecated. Please use the previous two cases instead.
 
 If you constructed a Nonlinear Solver with a sparse AD type, for example

docs/src/tutorials/large_systems.md

@@ -2,15 +2,15 @@
 
 This tutorial is for getting into the extra features of using NonlinearSolve.jl. Solving
 ill-conditioned nonlinear systems requires specializing the linear solver on properties of
-the Jacobian in order to cut down on the `\mathcal{O}(n^3)` linear solve and the
-`\mathcal{O}(n^2)` back-solves. This tutorial is designed to explain the advanced usage of
+the Jacobian in order to cut down on the ``\mathcal{O}(n^3)`` linear solve and the
+``\mathcal{O}(n^2)`` back-solves. This tutorial is designed to explain the advanced usage of
 NonlinearSolve.jl by solving the steady state stiff Brusselator partial differential
 equation (BRUSS) using NonlinearSolve.jl.
 
 ## Definition of the Brusselator Equation
 
 !!! note
-
+    
     Feel free to skip this section: it simply defines the example problem.
 
 The 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
 type. For example, a `SparseMatrixCSC` will give a sparse matrix. Other sparse matrix types
 include:
 
-- Bidiagonal
-- Tridiagonal
-- SymTridiagonal
-- BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
-- BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
+  - Bidiagonal
+  - Tridiagonal
+  - SymTridiagonal
+  - BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
+  - BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
 
 ## Approximate Sparsity Detection & Sparse Jacobians
 
@@ -167,7 +167,7 @@ and `u` and call `jacobian_sparsity` on our function with the example arguments,
 kick out a sparse matrix with our pattern, that we can turn into our `jac_prototype`.
 
 !!! tip
-
+    
     Alternatively you can use the `SparseConnectivityTracer.jl` package to automatically
     generate a sparse Jacobian.
 
@@ -224,7 +224,7 @@ choices, see the
 `linsolve` choices are any valid [LinearSolve.jl](https://linearsolve.sciml.ai/dev/) solver.
 
 !!! note
-
+    
     Switching to a Krylov linear solver will automatically change the nonlinear problem
     solver into Jacobian-free mode, dramatically reducing the memory required. This can be
     overridden by adding `concrete_jac=true` to the algorithm.
@@ -330,7 +330,7 @@ prob_brusselator_2d_exact_tracer = NonlinearProblem(
     u0, p; abstol = 1e-10, reltol = 1e-10)
 prob_brusselator_2d_approx_di = NonlinearProblem(
     NonlinearFunction(brusselator_2d_loop;
-        sparsity = DenseSparsityDetector(AutoForwardDiff(); atol=1e-4)),
+        sparsity = DenseSparsityDetector(AutoForwardDiff(); atol = 1e-4)),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
 @btime solve(prob_brusselator_2d_exact_symbolics, NewtonRaphson());