Add specialty integration methods (Phase 4)#6
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gvonness-apolitical merged 1 commit intomainfrom Feb 26, 2026
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…hase 4) Four new integration modules for handling difficult integrands: - tanh_sinh: Double-exponential quadrature for endpoint singularities (algebraic, logarithmic). Self-adaptive via level doubling. - cauchy_pv: Cauchy principal value integration via subtraction technique, using adaptive integration with automatic breakpoints. - oscillatory: Filon-Clenshaw-Curtis method for highly oscillatory integrands with sin/cos kernels. Chebyshev expansion with GL-computed modified moments. - weighted: Unified API for product integration dispatching to the appropriate Gaussian rule (Jacobi, Laguerre, Hermite, Chebyshev, LogWeight via Laguerre substitution).
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Summary
PV ∫f(x)/(x-c)dx = ∫[f(x)-f(c)]/(x-c)dx + f(c)·ln(...), using adaptive integration with automatic breakpoints at the pole.∫f(x)sin(ωx)dxand∫f(x)cos(ωx)dx. Chebyshev expansion of f at Clenshaw-Curtis nodes, modified Chebyshev moments computed via Gauss-Legendre quadrature. Falls back to adaptive integration for small ω.∫f(x)·w(x)dxdispatching to appropriate Gaussian rules (Jacobi, Laguerre, Hermite, Chebyshev). LogWeightw(x)=-ln(x)handled via Laguerre α=1 substitution.All modules follow the established builder pattern with convenience free functions.
Test plan
cargo clippyclean (no new warnings)cargo fmtapplied