Add 1D Allen-Cahn FD/IMEX playground: MMS study of BC-induced order reduction and boundary lifting (#637)

* Add Allen-Cahn 1D FD IMEX playground from scratch

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* Remove stray convergence plot from repo root

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* Clarify expected temporal convergence orders in run_convergence.py

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* Remove stray convergence plot from repo root

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* Add boundary-lifting variant and comparative temporal convergence study

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* Add MMS convergence study: hom/inhom BCs with manufactured sin/cos solutions

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* Add Part 4 to MMS study: parameter sets showing full convergence orders 3, 4, 5

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* Extend Part 4 to all three MMS classes with restol=1e-13; add _print_fc_table helper

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* Clean up: remove travelling-wave files, simplify run_convergence_mms.py to restol=1e-13 study only

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* WIP: plan 4th-order FD Laplacian

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* Replace 2nd-order FD Laplacian with 4th-order; use exact-solution comparison at nvars=255

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* Increase nvars to 1023 for clean inhomogeneous lift convergence orders

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* Remove mms acronym from file names, class names, and variable names

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Co-authored-by: pancetta <7158893+pancetta@users.noreply.github.com>

Author: Copilot