Complete DiffEqOperators deprecation updates (fixes #678)

- Fix typos in diffeq_operator.md (Opereators -> Operators, lienar -> linear, optimzations -> optimizations)
- Update page title to "Matrix-Free Linear Operators with SciMLOperators.jl"
- Add note in beeler_reuter.md suggesting MethodOfLines.jl and SciMLOperators.jl as alternatives to manual Laplacian implementation
- diffusion_implicit_heat_equation.md already uses SciMLOperators
- No remaining references to DiffEqOperators found in the documentation

This completes the deprecation of DiffEqOperators in favor of SciMLOperators.jl.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

docs/src/examples/beeler_reuter.md

@@ -92,6 +92,11 @@ end
 
 The finite-difference Laplacian is calculated in-place by a 5-point stencil. The Neumann boundary condition is enforced.
 
+!!! note
+    For more complex PDE discretizations, consider using [MethodOfLines.jl](https://docs.sciml.ai/MethodOfLines/stable/) 
+    which can automatically generate finite difference discretizations, or [SciMLOperators.jl](https://docs.sciml.ai/SciMLOperators/stable/) 
+    for defining matrix-free linear operators.
+
 ```julia
 # 5-point stencil
 function laplacian(Δu, u)

docs/src/features/diffeq_operator.md

@@ -1,6 +1,6 @@
-# Matrix-Free Linear Operators and Specializations on Linearity
+# Matrix-Free Linear Operators with SciMLOperators.jl
 
-SciML has the [SciMLOpereators.jl](https://docs.sciml.ai/SciMLOperators/stable/) library for defining linear operators.
-The ODE solvers will specialize on this property, for example using the lienar operators automatically with Newton-Krylov
-methods for matrix-free Newton-Krylov optimzations, but also allows for methods that requires knowing that part of the
+SciML has the [SciMLOperators.jl](https://docs.sciml.ai/SciMLOperators/stable/) library for defining linear operators.
+The ODE solvers will specialize on this property, for example using the linear operators automatically with Newton-Krylov
+methods for matrix-free Newton-Krylov optimizations, but also allows for methods that require knowing that part of the
 equation is linear, like exponential integrators. See the SciMLOperators.jl library for more information.