Books and Book Chapters

  1. Riemann--Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions, (T. Trogdon and S. Olver), SIAM, 2016 Sample .pdf
  2. A Unified Numerical Approach for the Nonlinear Schrodinger Equations, (T. Trogdon). Unified transform method for boundary value problems: applications and advances , (B. Pelloni and A. S. Fokas (Eds.)), SIAM, 2015.


  1. Riemann--Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions .pdf (.pdf with front matter)

Numerical Analysis and Approximation Theory

  1. Benchmarking numerical methods for lattice equations using the Toda lattice, submitted, (D. Bilman and T. Trogdon). .pdf
  2. Smoothed analysis for the conjugate gradient algorithm , SIGMA, 2016, Vol. 12, (G. Menon and T. Trogdon). .pdf
  3. Fast computation of Gauss quadrature nodes and weights on the whole real line , IMA J. Numer. Anal., 2016, Vol. 36, (A. Townsend, T. Trogdon and S. Olver). .pdf
  4. Rational approximation, oscillatory Cauchy integrals and Fourier transforms, Constr. Approx., 2016, Vol. 43, (T. Trogdon). .pdf
  5. A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature , IMA J. Numer. Anal., Vol. 36, (T. Trogdon and S. Olver). .pdf
  6. On the application of GMRES to oscillatory singular integral equations , BIT Numer. Math., 2015, Vol. 55, (T. Trogdon). .pdf
  7. Nonlinear steepest descent and the numerical solution of Riemann-Hilbert problems, Comm. Pure Appl. Math., 2014, Vol. 67, (S. Olver and T. Trogdon). .pdf

Probability and Random Matrix Theory

  1. The conjugate gradient algorithm on well-condition Wishart matrices is almost deterministic, submitted, (P. Deift and T. Trogdon). arXiv
  2. On spectral and numerical properties of random butterfly matrices, submitted, (T. Trogdon). .pdf
  3. Universality in numerical computation with random data. Case studies, analytic results and some spectulations, submitted, (P. Deift and T. Trogdon). .pdf
  4. Random matrices and the New York City subway system, Phys. Rev. E, Vol. 96, (A. Jagannath and T. Trogdon). .pdf
  5. Universality for eigenvalue algorithms on sample covariance matrices, SIAM J. Numer. Anal., to appear, (P. Deift and T. Trogdon). .pdf
  6. Universality for the Toda algorithm to compute the eigenvalues of a random matrix, CPAM, to appear, (P. Deift and T. Trogdon). .pdf
  7. Universality in halting time and its applications in optimization, Q. Appl. Math., to appear, (L. Sagun, T. Trogdon and Y. LeCun). .pdf
  8. On the condition number of the critically-scaled Laguerre Unitary Ensemble, DCDS-A, 2016, (P. Deift, G. Menon and T. Trogdon). .pdf
  9. An extension of the Derrida-Lebowitz-Speer-Spohn equation, Phys. Lett. A, 2015, (C. Bordenave, P. Germain and T. Trogdon). .pdf
  10. Universality in Numerical Computations with Random Data, PNAS, 2014, Vol. 111, (P. Deift, G. Menon, S. Olver and T. Trogdon). .pdf
  11. Sampling Unitary Ensembles, Random Matrices Theory Appl., 2015, Vol. 4, (S. Olver, R. R. Nadakuditi and T. Trogdon). .pdf
  12. Numerical solution of Riemann--Hilbert problems: orthogonal polynomials and random matrix theory, Constr. Approx., 2014, Vol. 39, (S. Olver and T. Trogdon). .pdf

Linear PDEs

  1. Boundary value problems for evolution partial differential equations with discontinuous data, submitted, (G. Biondini and T. Trogdon). .pdf
  2. Gibbs phenomenon for dispersive PDEs on the line, SIAM J. Appl. Math., Vol. 77, (G. Biondini and T. Trogdon). .pdf
  3. The Method of Fokas for Solving Linear Partial Differential Equations, SIAM Review, 2014, Vol. 56, (B. Deconinck, T. Trogdon and V. Vasan). .pdf
  4. The solution of Linear Constant-Coefficient Evolution PDEs With Periodic Boundary Conditions, Applicable Analysis, 2012, Vol. 91, (T. Trogdon and B. Deconinck). .pdf

Integrable Systems and Inverse Scattering

  1. On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data, submitted for publication, (D. Bilman and T. Trogdon). arXiv
  2. Numerical inverse scattering for the sine--Gordon equation, submitted for publication, (B. Deconinck, T. Trogdon and X. Yang). arXiv
  3. Numerical inverse scattering for the Toda lattice, submitted for publication, (D. Bilman and T. Trogdon). .pdf
  4. Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results, Physics Letters A, 2014, Vol. 378, (T. Trogdon and B. Deconinck). .pdf
  5. A numerical dressing method for the nonlinear superposition of solutions of the KdV equation, Nonlinearity, 2013, Vol. 27, (T. Trogdon and B. Deconinck). .pdf
  6. Numerical computation of the finite-genus solutions of the Korteweg--de Vries equation via Riemann--Hilbert problems , Appl. Math. Lett., 2013, Vol. 16, (T. Trogdon and B. Deconinck). .pdf
  7. A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution, Physica D, 2013, Vol. 251, (T. Trogdon and B. Deconinck). .pdf
  8. Numerical inverse scattering for the focusing and defocusing nonlinear Schrodinger equations, Proc. Roy. Soc. Lon. A., 2012, (T. Trogdon and S. Olver). .pdf
  9. Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations, Physica D, 2012,(T. Trogdon, S. Olver and B. Deconinck). .pdf

Optical Physics

  1. Neck instability of bright solitary waves in hyperbolic Kerr media, Optics Letters, 2013,(S.-P. Gorza, B. Deconinck, T. Trogdon, P. Emplit and M. Haelterman). .pdf
  2. Experimental demonstration of the oscillatory snake instability of the bright soliton of the (2+1)D hyperbolic nonlinear Schrodinger equation, Physical Review Letters, 2011, (S.-P. Gorza, P. Emplit, T. Trogdon, B. Deconinck and M. Haelterman). .pdf
  3. Transverse Instability of Bright Solitons in Hyperbolic dispersive Media, in Nonlinear Photonics, OSA Technical Digest, 2010,(S.-P. Gorza, M. Haelterman, P. Emplit, T. Trogdon and B. Deconinck)..pdf