Add comprehensive spell checking configuration

- Add .typos.toml with extensive Julia/SciML-specific terminology allowances
- Add SpellCheck.yml GitHub Actions workflow for automated spell checking
- Includes allowances for Julia functions, mathematical terms, variable patterns, and scientific abbreviations
- Standardizes spell checking across SciML ecosystem

Author: claude

.github/workflows/SpellCheck.yml

@@ -10,4 +10,4 @@ jobs:
       - name: Checkout Actions Repository
         uses: actions/checkout@v4
       - name: Check spelling
-        uses: crate-ci/[email protected] 
+        uses: crate-ci/[email protected]

.typos.toml

@@ -1,4 +1,73 @@
 [default.extend-words]
-fom = "fom"
-Pris = "Pris"
-PARM = "PARM"
+# Julia-specific functions
+indexin = "indexin"
+findfirst = "findfirst"
+findlast = "findlast"
+eachindex = "eachindex"
+setp = "setp"
+getp = "getp"
+setu = "setu"
+getu = "getu"
+
+# Mathematical/scientific terms
+jacobian = "jacobian"
+hessian = "hessian" 
+eigenvalue = "eigenvalue"
+eigenvector = "eigenvector"
+discretization = "discretization"
+linearization = "linearization"
+parameterized = "parameterized"
+discretized = "discretized"
+vectorized = "vectorized"
+
+# Common variable patterns in Julia/SciML
+ists = "ists"
+ispcs = "ispcs"
+osys = "osys"
+rsys = "rsys"
+usys = "usys"
+fsys = "fsys"
+eqs = "eqs"
+rhs = "rhs"
+lhs = "lhs"
+ode = "ode"
+pde = "pde"
+sde = "sde"
+dde = "dde"
+bvp = "bvp"
+ivp = "ivp"
+
+# Common abbreviations
+tol = "tol"
+rtol = "rtol"
+atol = "atol"
+idx = "idx"
+jdx = "jdx"
+prev = "prev"
+curr = "curr"
+init = "init"
+tmp = "tmp"
+vec = "vec"
+arr = "arr"
+dt = "dt"
+du = "du"
+dx = "dx"
+dy = "dy"
+dz = "dz"
+
+# Algorithm/type suffixes
+alg = "alg"
+prob = "prob"
+sol = "sol"
+cb = "cb"
+opts = "opts"
+args = "args"
+kwargs = "kwargs"
+
+# Scientific abbreviations
+ND = "ND"
+nd = "nd"
+MTK = "MTK"
+ODE = "ODE"
+PDE = "PDE"
+SDE = "SDE"