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        "distributed-fields"
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        "chebyshev-reference"
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        "strong-types",
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      "target": "world_strong_types_example",
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        "domain",
        "strong-types",
        "coordinates"
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      "target": "write_results",
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      "capabilities": [
        "binary-writer",
        "binary-reader",
        "mpi-io",
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  "book": [
    {
      "program": 1,
      "title": "convergence of fourth-order finite differences",
      "source": "https://people.maths.ox.ac.uk/trefethen/p1.m",
      "chapter": "differentiation/periodic/index.qmd",
      "scope": "Original fourth-order finite-difference resolution family, with additional FD2 and FFT comparisons."
    },
    {
      "program": 2,
      "title": "convergence of periodic spectral method (compare p1.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p2.m",
      "chapter": "differentiation/smoothness/index.qmd",
      "scope": "Original even 2..100 collocation matrix sweep; FFT comparison added."
    },
    {
      "program": 3,
      "title": "band-limited interpolation",
      "source": "https://people.maths.ox.ac.uk/trefethen/p3.m",
      "chapter": "interpolation/cardinal/index.qmd",
      "scope": "All three original sampled profiles and sinc reconstructions; exact nodal limits handled."
    },
    {
      "program": 4,
      "title": "periodic spectral differentiation",
      "source": "https://people.maths.ox.ac.uk/trefethen/p4.m",
      "chapter": "differentiation/collocation/index.qmd",
      "scope": "Original periodic cotangent differentiation of hat and analytic profiles."
    },
    {
      "program": 5,
      "title": "repetition of p4.m via FFT",
      "source": "https://people.maths.ox.ac.uk/trefethen/p5.m",
      "chapter": "differentiation/collocation/index.qmd",
      "scope": "FFT version of both program 4 profiles, compared against the matrix action."
    },
    {
      "program": 6,
      "title": "variable coefficient wave equation",
      "source": "https://people.maths.ox.ac.uk/trefethen/p6.m",
      "chapter": "waves/variable-transport/index.qmd",
      "scope": "Original variable-speed Gaussian experiment and book startup preset, with a consistent Taylor startup and characteristic reference added."
    },
    {
      "program": 7,
      "title": "accuracy of periodic spectral differentiation",
      "source": "https://people.maths.ox.ac.uk/trefethen/p7.m",
      "chapter": "differentiation/smoothness/index.qmd",
      "scope": "All four original regularity profiles on even 6..50 grids, with matrix and FFT errors."
    },
    {
      "program": 8,
      "title": "eigenvalues of harmonic oscillator -u\"+x^2 u on R",
      "source": "https://people.maths.ox.ac.uk/trefethen/p8.m",
      "chapter": "fourier/harmonic-oscillator/index.qmd",
      "scope": "Original L=8 and N=6:6:36 harmonic oscillator, with kinetic matrix built using native LocalFFT."
    },
    {
      "program": 9,
      "title": "polynomial interpolation in equispaced and Chebyshev pts",
      "source": "https://people.maths.ox.ac.uk/trefethen/p9.m",
      "chapter": "polynomials/interpolation/index.qmd",
      "scope": "Original degree-16 node comparison, using barycentric evaluation instead of monomial fitting."
    },
    {
      "program": 10,
      "title": "polynomials and corresponding equipotential curves",
      "source": "https://people.maths.ox.ac.uk/trefethen/p10.m",
      "chapter": "polynomials/nodal-polynomials/index.qmd",
      "scope": "Original signed nodal products and complex-plane magnitude contours, evaluated directly from their roots."
    },
    {
      "program": 11,
      "title": "Chebyshev differentation of a smooth function",
      "source": "https://people.maths.ox.ac.uk/trefethen/p11.m",
      "chapter": "polynomials/differentiation/index.qmd",
      "scope": "Original smooth profile at degrees 10 and 20, differentiated with the Chebyshev collocation matrix."
    },
    {
      "program": 12,
      "title": "accuracy of Chebyshev spectral differentiation",
      "source": "https://people.maths.ox.ac.uk/trefethen/p12.m",
      "chapter": "polynomials/regularity/index.qmd",
      "scope": "All four original profiles and degrees 1..50, with limiting bump values handled explicitly."
    },
    {
      "program": 13,
      "title": "solve linear BVP u_xx = exp(4x), u(-1)=u(1)=0",
      "source": "https://people.maths.ox.ac.uk/trefethen/p13.m",
      "chapter": "polynomials/boundary-values/index.qmd",
      "scope": "Original degree-16 homogeneous Dirichlet collocation problem, solved with native GMRES."
    },
    {
      "program": 14,
      "title": "solve nonlinear BVP u_xx = exp(u), u(-1)=u(1)=0",
      "source": "https://people.maths.ox.ac.uk/trefethen/p14.m",
      "chapter": "polynomials/nonlinear-boundary/index.qmd",
      "scope": "Original nonlinear collocation problem, using native Newton–GMRES instead of fixed-point iteration and an analytic reference."
    },
    {
      "program": 15,
      "title": "solve eigenvalue BVP u_xx = lambda*u, u(-1)=u(1)=0",
      "source": "https://people.maths.ox.ac.uk/trefethen/p15.m",
      "chapter": "polynomials/eigenmodes/index.qmd",
      "scope": "Original degree-36 Dirichlet spectrum and six selected modes, using an example-owned complex QR eigensolver."
    },
    {
      "program": 16,
      "title": "Poisson eq. on [-1,1]x[-1,1] with u=0 on boundary",
      "source": "https://people.maths.ox.ac.uk/trefethen/p16.m",
      "chapter": "polynomials/poisson-square/index.qmd",
      "scope": "Original degree-24 Chebyshev Poisson problem; native GMRES applies the tensor operator without forming a Kronecker matrix."
    },
    {
      "program": 17,
      "title": "Helmholtz eq. u_xx + u_yy + (k^2)u = f",
      "source": "https://people.maths.ox.ac.uk/trefethen/p17.m",
      "chapter": "polynomials/helmholtz-square/index.qmd",
      "scope": "Original k=9 degree-24 Helmholtz problem with a native tensor-action GMRES solve."
    },
    {
      "program": 18,
      "title": "Chebyshev differentiation via FFT (compare p11.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p18.m",
      "chapter": "polynomials/differentiation/index.qmd",
      "scope": "Same polynomial derivative via native LocalFFT cosine coefficients, with explicit O(N²) coefficient-sum evaluation and endpoint limits."
    },
    {
      "program": 19,
      "title": "2nd-order wave eq. on Chebyshev grid (compare p6.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p19.m",
      "chapter": "waves/chebyshev-line/index.qmd",
      "scope": "FFT-based Chebyshev wave with the original N=80 Gaussian, leapfrog startup and rounded save schedule; direct chain-rule second derivatives replace two successive chebfft calls. Taylor startup and an exact standing mode are additional checks."
    },
    {
      "program": 20,
      "title": "2nd-order wave eq. in 2D via FFT (compare p19.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p20.m",
      "chapter": "waves/chebyshev-square/index.qmd",
      "scope": "Original N=24 Chebyshev square, Gaussian and leapfrog startup. Native LocalFFT evaluates both tensor derivatives; initial Gaussian boundary tails are retained. Nodal plots replace cubic display interpolation; Taylor startup exposes the initial-velocity error."
    },
    {
      "program": 21,
      "title": "eigenvalues of Mathieu operator -u_xx + 2qcos(2x)u",
      "source": "https://people.maths.ox.ac.uk/trefethen/p21.m",
      "chapter": "fourier/mathieu/index.qmd",
      "scope": "Original N=42 and q=0:.2:15 Mathieu sweep; native LocalFFT plus example-owned symmetric Jacobi diagonalization."
    },
    {
      "program": 22,
      "title": "5th eigenvector of Airy equation u_xx = lambda*x*u",
      "source": "https://people.maths.ox.ac.uk/trefethen/p22.m",
      "chapter": "polynomials/airy/index.qmd",
      "scope": "Original four-degree Airy experiment; explicitly eliminate the zero-weight constraint before a finite eigenproblem."
    },
    {
      "program": 23,
      "title": "eigenvalues of perturbed Laplacian on [-1,1]x[-1,1]",
      "source": "https://people.maths.ox.ac.uk/trefethen/p23.m",
      "chapter": "polynomials/membrane/index.qmd",
      "scope": "Original degree-16 perturbed-square Laplacian and four low modes with example-owned dense QR."
    },
    {
      "program": 24,
      "title": "pseudospectra of Davies's complex harmonic oscillator",
      "source": "https://people.maths.ox.ac.uk/trefethen/p24.m",
      "chapter": "polynomials/pseudospectra/index.qmd",
      "scope": "Original degree 70, half-length 6, all 69 eigenvalues and 26 by 21 complex grid with increments of two. Native Chebyshev derivatives; one-sided complex Jacobi singular values avoid normal equations. Complete original grid independently qualified."
    },
    {
      "program": 25,
      "title": "stability regions for ODE formulas",
      "source": "https://people.maths.ox.ac.uk/trefethen/p25.m",
      "chapter": "integration/stability/index.qmd",
      "scope": "Original AB/AM/BDF root-locus families and RK stability boundaries; native RK tableaus plus example-owned multistep references."
    },
    {
      "program": 26,
      "title": "eigenvalues of 2nd-order Chebyshev diff. matrix",
      "source": "https://people.maths.ox.ac.uk/trefethen/p26.m",
      "chapter": "polynomials/eigenmodes/index.qmd",
      "scope": "Original degree-60 spectrum and grid-scale mode; physical mode labelled and selected consistently as N/4."
    },
    {
      "program": 27,
      "title": "Solve KdV eq. u_t + uu_x + u_xxx = 0 on [-pi,pi] by",
      "source": "https://people.maths.ox.ac.uk/trefethen/p27.m",
      "chapter": "waves/kdv/index.qmd",
      "scope": "Original N=256 periodic two-pulse KdV experiment, timestep, unfiltered nonlinear product and zero odd Nyquist multipliers. Native complex-state RK4 integrates a global integrating factor, algebraically equivalent to the book's per-step stage formula; complete fields and integral diagnostics are saved."
    },
    {
      "program": 28,
      "title": "eigenmodes of Laplacian on the disk (compare p22.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p28.m",
      "chapter": "polynomials/disk-modes/index.qmd",
      "scope": "Original N25,M20 disk Laplacian, complete 240-mode spectrum with angular multiplicity, selected modes 1,3,6,10 and frequency ratios. Native Chebyshev derivatives and equivalent Fourier radial blocks; Bessel references and full-matrix qualification. Polar fields with nodal lines replace wireframe projection."
    },
    {
      "program": 29,
      "title": "solve Poisson equation on the unit disk",
      "source": "https://people.maths.ox.ac.uk/trefethen/p29.m",
      "chapter": "polynomials/poisson-disk/index.qmd",
      "scope": "Original N31,M40 forcing and zero-boundary disk solution. Native FFT separation and GMRES solve the equivalent original polar matrix; exact separated and smooth manufactured references, N63 radial refinement and independent full-matrix qualification. Non-smooth pole forcing is explicit."
    },
    {
      "program": 30,
      "title": "spectral integration, ODE style (compare p12.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p30.m",
      "chapter": "polynomials/integration/index.qmd",
      "scope": "Original antiderivative collocation experiment for four profiles and degrees 1..50; native GMRES replaces the explicit inverse."
    },
    {
      "program": 31,
      "title": "gamma function via complex integral, trapezoid rule",
      "source": "https://people.maths.ox.ac.uk/trefethen/p31.m",
      "chapter": "quadrature/complex-contour/index.qmd",
      "scope": "Original 70-point circular gamma contour and complex rectangle; retain reciprocal estimates and explicitly mark poles."
    },
    {
      "program": 32,
      "title": "solve u_xx = exp(4x), u(-1)=0, u(1)=1 (compare p13.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p32.m",
      "chapter": "polynomials/boundary-values/index.qmd",
      "scope": "Original nonzero Dirichlet problem with an affine lift and native GMRES."
    },
    {
      "program": 33,
      "title": "solve linear BVP u_xx = exp(4x), u'(-1)=u(1)=0",
      "source": "https://people.maths.ox.ac.uk/trefethen/p33.m",
      "chapter": "polynomials/boundary-values/index.qmd",
      "scope": "Original mixed Neumann/Dirichlet problem with a derivative row and native GMRES."
    },
    {
      "program": 34,
      "title": "Allen-Cahn eq. u_t = eps*u_xx+u-u^3, u(-1)=-1, u(1)=1",
      "source": "https://people.maths.ox.ac.uk/trefethen/p34.m",
      "chapter": "polynomials/allen-cahn-fixed/index.qmd",
      "scope": "Original degree-20 Allen–Cahn equation, epsilon=.01, fixed endpoints, lifted full Chebyshev D2 and explicit Euler through t=100. Native EulerStepper advances the vector; barycentric interpolation replaces monomial display fitting. An operator-based timestep cap applies to refinements and preserves the original degree-20 default."
    },
    {
      "program": 35,
      "title": "Allen-Cahn eq. as in p34.m, but with boundary condition",
      "source": "https://people.maths.ox.ac.uk/trefethen/p35.m",
      "chapter": "polynomials/allen-cahn-driven/index.qmd",
      "scope": "Original degree-20 Allen–Cahn equation with u(1,t)=1+sin(t/5)^2, full Chebyshev D2, and explicit endpoint replacement after every Euler step through t=100. Native EulerStepper and barycentric display evaluation preserve the discrete evolution. An operator-based timestep cap applies to refinements and preserves the original degree-20 default."
    },
    {
      "program": 36,
      "title": "Laplace eq. on [-1,1]x[-1,1] with nonzero BCs",
      "source": "https://people.maths.ox.ac.uk/trefethen/p36.m",
      "chapter": "polynomials/laplace-square/index.qmd",
      "scope": "Original degree-24 nonzero-boundary Laplace problem; equivalent boundary elimination replaces identity boundary rows."
    },
    {
      "program": 37,
      "title": "2D \"wave tank\" with Neumann BCs for |y|=1",
      "source": "https://people.maths.ox.ac.uk/trefethen/p37.m",
      "chapter": "waves/mixed-tank/index.qmd",
      "scope": "Original A=3, Nx=50, Ny=15 wave tank, Gaussian, nominal-step startup and Neumann reconstruction after each leapfrog update. FFT actions replace equivalent dense Fourier/Chebyshev matrices. Exact standing-mode and Taylor-start presets are additional checks."
    },
    {
      "program": 38,
      "title": "solve u_xxxx = exp(x), u(-1)=u(1)=u'(-1)=u'(1)=0",
      "source": "https://people.maths.ox.ac.uk/trefethen/p38.m",
      "chapter": "polynomials/clamped-beam/index.qmd",
      "scope": "Original degree-15 clamped fourth-order problem. Native Chebyshev nodes/derivatives construct the weighted operator; native GMRES replaces backslash, and barycentric reconstruction of the auxiliary polynomial preserves zero values and slopes. Complete values and slopes are checked against an independently determined analytic solution."
    },
    {
      "program": 39,
      "title": "eigenmodes of biharmonic on a square with clamped BCs",
      "source": "https://people.maths.ox.ac.uk/trefethen/p39.m",
      "chapter": "polynomials/clamped-plate/index.qmd",
      "scope": "All 25 degree-17 clamped square-plate modes and relative frequencies; native Chebyshev D4 and the original interior D2 tensor operator. Symmetry blocks preserve repeated modes; constrained barycentric display replaces cubic image interpolation."
    },
    {
      "program": 40,
      "title": "eigenvalues of Orr-Sommerfeld operator (compare p38.m)",
      "source": "https://people.maths.ox.ac.uk/trefethen/p40.m",
      "chapter": "polynomials/orr-sommerfeld/index.qmd",
      "scope": "Original R=5772 and degrees 40,60,80,100; native Chebyshev D4/D2 construction and complete complex generalized spectra. Pivoted mass solves plus example-owned shifted QR replace a generalized eigensolver; original-pencil residuals and independent qualification are explicit."
    }
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