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feat(bvp): add finite-difference boundary-value solver - #18
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Add an interactive second-order boundary value problem solver with finite-difference discretization, Thomas forward/backward traces, residual checks, plot, and localized UI.
Add a one-click equation example, tighten responsive form sizing, and use clearer Uzbek terminology for the boundary value and sweep methods.
Allow entering the equation, step size, interval endpoints, and boundary conditions as a single multiline problem statement, then parse them into the solver inputs.
Make individual compact parameter fields the primary form, add a dedicated h input that derives the interval count, and move full-statement parsing into an optional disclosure.
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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Description
Adds a finite-difference boundary-value solver using the Thomas algorithm, natural-language equation and boundary-condition parsing, and a worked derivation/notebook view with copy support. Updates the BVP navigation ordering and Uzbek, Russian, and English translations.
Type of Change
Mathematical & Technical Verification
y'' - 2(1 + x^2)y = 0,y(0) = 0,y(0.8) = 3.5,h = 0.1parses to 8 intervals and 9 nodes; the solver returns the imposed endpoint value3.5.Checklist
any).bun run lintexits with code 0.bun run buildsucceeds without errors.uz,ru,en).Validation results:
& $env:APPDATA\npm\bun.cmd run lint— PASS; BVP parser/solver runtime check — PASS (8 intervals, 9 nodes, endpoint 3.5); JSON parsing for all three locale files — PASS.& $env:APPDATA\npm\bun.cmd run build— NOT RUN (the build tool invocation was denied).