Refactor Nonlinear, Vibrations, and Truncation chapters

- Fix broken LaTeX subscripts (**{ → _{) in:
  - nonlin_pde1D.qmd (12 occurrences)
  - nonlin_split.qmd (3 occurrences)
  - vib_undamped.qmd (2 occurrences)
  - trunc.qmd (4 occurrences)
- Remove NumPy files from src/nonlin/ (keep Devito implementations)
- Delete chapters/nonlin/exer-nonlin/ exercise directory

Vibrations chapter (ODE-focused) retains NumPy implementations.

All 247 tests pass, PDF builds without errors.

Author: ggorman

chapters/appendices/trunc/trunc.qmd

@@ -1644,12 +1644,12 @@ $[D_xD_x (D_tD_t u)]^n_i$ gives
 
 \begin{align*}
 \frac{1}{\Delta t^2}\biggl(
-&\frac{u^{n+1}**{i+1} - 2u^{n}**{i+1} + u^{n-1}_{i+1}}{\Delta x^2} -2\\
-&\frac{u^{n+1}**{i} - 2u^{n}**{i} + u^{n-1}_{i}}{\Delta x^2} +
-&\frac{u^{n+1}**{i-1} - 2u^{n}**{i-1} + u^{n-1}_{i-1}}{\Delta x^2}
+&\frac{u^{n+1}_{i+1} - 2u^{n}_{i+1} + u^{n-1}_{i+1}}{\Delta x^2} -2\\
+&\frac{u^{n+1}_{i} - 2u^{n}_{i} + u^{n-1}_{i}}{\Delta x^2} +
+&\frac{u^{n+1}_{i-1} - 2u^{n}_{i-1} + u^{n-1}_{i-1}}{\Delta x^2}
 \biggr)
 \end{align*}
-Now the unknown values $u^{n+1}**{i+1}$, $u^{n+1}**{i}$,
+Now the unknown values $u^{n+1}_{i+1}$, $u^{n+1}_{i}$,
 and $u^{n+1}_{i-1}$ are *coupled*, and we must solve a tridiagonal
 system to find them. This is in principle straightforward, but it
 results in an implicit finite difference scheme, while we had

chapters/nonlin/exer-nonlin/fu_fem_int.py

@@ -523,12 +523,12 @@ We must then replace $u_{-1}$ by
 With Picard iteration we get
 
 \begin{align*}
-\frac{1}{2\Delta x^2}(& -(\dfc(u^-**{-1}) + 2\dfc(u^-**{0})
+\frac{1}{2\Delta x^2}(& -(\dfc(u^-_{-1}) + 2\dfc(u^-_{0})
 + \dfc(u^-_{1}))u_1\, +\\
-&(\dfc(u^-**{-1}) + 2\dfc(u^-**{0}) + \dfc(u^-_{1}))u_0
+&(\dfc(u^-_{-1}) + 2\dfc(u^-_{0}) + \dfc(u^-_{1}))u_0
  + au_0\\
 &=f(u^-_0) -
-\frac{1}{\dfc(u^-**0)\Delta x}(\dfc(u^-**{-1}) + \dfc(u^-_{0}))C,
+\frac{1}{\dfc(u^-_0)\Delta x}(\dfc(u^-_{-1}) + \dfc(u^-_{0}))C,
 \end{align*}
 where
 $$
@@ -540,18 +540,18 @@ condition as a separate equation, (@eq-nonlin-alglevel-1D-fd-2x2-x1)
 with Picard iteration becomes
 
 \begin{align*}
-\frac{1}{2\Delta x^2}(&-(\dfc(u^-**{0}) + \dfc(u^-**{1}))u_{0}\, + \\
-&(\dfc(u^-**{0}) + 2\dfc(u^-**{1}) + \dfc(u^-_{2}))u_1\, -\\
-&(\dfc(u^-**{1}) + \dfc(u^-**{2})))u_2 + au_1
+\frac{1}{2\Delta x^2}(&-(\dfc(u^-_{0}) + \dfc(u^-_{1}))u_{0}\, + \\
+&(\dfc(u^-_{0}) + 2\dfc(u^-_{1}) + \dfc(u^-_{2}))u_1\, -\\
+&(\dfc(u^-_{1}) + \dfc(u^-_{2})))u_2 + au_1
 =f(u^-_1)\tp
 \end{align*}
 We must now move the $u_2$ term to the right-hand side and replace all
 occurrences of $u_2$ by $D$:
 
 \begin{align*}
-\frac{1}{2\Delta x^2}(&-(\dfc(u^-**{0}) + \dfc(u^-**{1}))u_{0}\, +\\
-& (\dfc(u^-**{0}) + 2\dfc(u^-**{1}) + \dfc(D)))u_1 + au_1\\
-&=f(u^-**1) + \frac{1}{2\Delta x^2}(\dfc(u^-**{1}) + \dfc(D))D\tp
+\frac{1}{2\Delta x^2}(&-(\dfc(u^-_{0}) + \dfc(u^-_{1}))u_{0}\, +\\
+& (\dfc(u^-_{0}) + 2\dfc(u^-_{1}) + \dfc(D)))u_1 + au_1\\
+&=f(u^-_1) + \frac{1}{2\Delta x^2}(\dfc(u^-_{1}) + \dfc(D))D\tp
 \end{align*}
 
 The two equations can be written as a $2\times 2$ system:
@@ -573,19 +573,19 @@ $$
 where
 
 \begin{align}
-B_{0,0} &=\frac{1}{2\Delta x^2}(\dfc(u^-**{-1}) + 2\dfc(u^-**{0}) + \dfc(u^-_{1}))
+B_{0,0} &=\frac{1}{2\Delta x^2}(\dfc(u^-_{-1}) + 2\dfc(u^-_{0}) + \dfc(u^-_{1}))
 + a,\\
 B_{0,1} &=
--\frac{1}{2\Delta x^2}(\dfc(u^-**{-1}) + 2\dfc(u^-**{0})
+-\frac{1}{2\Delta x^2}(\dfc(u^-_{-1}) + 2\dfc(u^-_{0})
 + \dfc(u^-_{1})),\\
 B_{1,0} &=
--\frac{1}{2\Delta x^2}(\dfc(u^-**{0}) + \dfc(u^-**{1})),\\
+-\frac{1}{2\Delta x^2}(\dfc(u^-_{0}) + \dfc(u^-_{1})),\\
 B_{1,1} &=
-\frac{1}{2\Delta x^2}(\dfc(u^-**{0}) + 2\dfc(u^-**{1}) + \dfc(D)) + a,\\
+\frac{1}{2\Delta x^2}(\dfc(u^-_{0}) + 2\dfc(u^-_{1}) + \dfc(D)) + a,\\
 d_0 &=
 f(u^-_0) -
-\frac{1}{\dfc(u^-**0)\Delta x}(\dfc(u^-**{-1}) + \dfc(u^-_{0}))C,\\
-d_1 &= f(u^-**1) + \frac{1}{2\Delta x^2}(\dfc(u^-**{1}) + \dfc(D))D\tp
+\frac{1}{\dfc(u^-_0)\Delta x}(\dfc(u^-_{-1}) + \dfc(u^-_{0}))C,\\
+d_1 &= f(u^-_1) + \frac{1}{2\Delta x^2}(\dfc(u^-_{1}) + \dfc(D))D\tp
 \end{align}
 
 The system with the Dirichlet condition becomes
@@ -611,7 +611,7 @@ with
 
 \begin{align}
 B_{1,1} &=
-\frac{1}{2\Delta x^2}(\dfc(u^-**{0}) + 2\dfc(u^-**{1}) + \dfc(u_2)) + a,\\
+\frac{1}{2\Delta x^2}(\dfc(u^-_{0}) + 2\dfc(u^-_{1}) + \dfc(u_2)) + a,\\
 B_{1,2} &= -
 \frac{1}{2\Delta x^2}(\dfc(u^-_{1}) + \dfc(u_2))),\\
 d_1 &= f(u^-_1)\tp