Professor of Mathematics

University of Michigan

530 Church Street

Ann Arbor, MI 48103

email: divakar(at)umich(dot)edu

BTech in Computer Science and Engineering, IIT Bombay, 1992

PhD in Computer Science, Cornell University, 1998

Much of my research is in numerical analysis and nonlinear dynamics. In 2016, I started working in mathematical genetics.

**Scientific Programming and Computer Architechture**

MIT Press, 2017

ISBN 9780262036290

Book website and code repository

The book website includes the complete text of the book in html

- R. Navarrete and D. Viswanath, Delay embedding of periodic orbits using a fixed observation function. pdf. Physica D, Vol. 388, 2019, p. 1-9.
- A. Melfi and D. Viswanath, The Wright-Fisher site frequency spectrum as a perturbation of the coalescent's. pdf. Theoretical Population Biology, Vol. 124, 2018, p. 81-92.
- A. Melfi and D. Viswanath, Single and simultaneous binary mergers in Wright-Fisher genealogies. pdf.Theoretical Population Biology, Vol. 121, 2018, p. 60-71.
- R. Navarrete and D. Viswanath, Prediction of dynamical time series using kernel based regression and smooth splines. pdf. Electronic Journal of Statistics, Vol. 12, 2018, p. 2217-2237.
- R. Navarrete and D. Viswanath, Accuracy and stability of inversion of power series. pdf. IMA J. of Numerical Analysis, Volume 36, Issue 1, 1 January 2016, p. 421–436.
- D. Viswanath, Spectral integration of linear boundary value problems. pdf. Journal of Computational and Applied Mathematics, Volume 36, 2015, p. 421–436.
- D. Viswanath and I. Tobasco, Navier–Stokes solver using Green’s functions I: Channel flow and plane Couette flow. pdf. Journal of Computational Physics, vol. 251 (2013), p. 414–431.
- B. Sadiq and D. Viswanath, Barycentric Hermite interpolation. pdf. SIAM Journal on Scientific Computing, vol. 35 (2013), p. A1254-A1270
- D. Viswanath, K. Serkh and X. Liang, Metric entropy and the optimal prediction of chaotic signals. pdf. SIAM Journal on Applied Dynamical Systems, vol. 12 (2013), p. 1085-1113.
- B. Sadiq and D. Viswanath, Finite difference weights, spectral differentiation, and superconvergence. pdf. Mathematics of Computation, vol. 83 (2014), p. 2403–2427.
- Y. Charles Li and D. Viswanath, Exact and asymptotic conditions on traveling wave solutions of the Navier-Stokes Equations. pdf. Physics of Fluids, vol. 21 (2009), 101703.
- D. Viswanath and S. Şahutoğlu, Complex singularities and the Lorenz attractor. pdf. SIAM Review, vol. 52 (2010), p. 294-314.
- D. Viswanath and P. Cvitanović, Stable manifolds and the transition to turbulence in pipe flow. pdf. J. Fluid Mech., vol. 627 (2009), p. 215-233. J. Fluid Mech., vol. 627 (2009), p. 215-233.
- J. Halcrow, J.F. Gibson, P. Cvitanović and D. Viswanath, Heteroclinic connections in plane Couette flow. pdf. J. Fluid Mech., vol. 611 (2009), p. 365-376.
- D. Viswanath, The critical layer in pipe flow at high Reynolds number. pdf. Phil. Trans. Roy. Soc., vol. 367 (2009).
- D. Viswanath, The dynamics of transition to turbulence in plane Couette flow. pdf. Mathematics and computation: a contemporary view. The Abel Symosium 2006. Springer-Verlag. Berlin. 2008.
- D. Viswanath, Recurrent motions within plane Couette turbulence. pdf. J. Fluid Mech., 580 (2007), 339-358.
- M. Conger and D. Viswanath, Shuffling cards for blackjack, bridge, and other card games. arxiv.
- D. Viswanath, Stable manifolds and homoclinic points near resonances in the restricted three-body problem. pdf. Celestial Mechanics and Dynamical Astronomy, 94 (2006), 213-235.
- M. Conger and D. Viswanath, Normal approximations for descents and inversions of permutations of multisets. pdf. J. Theor. Probab., 20 (2007), 309-325.
- D. Viswanath, Linear stability analysis of resonant periodic motions in the restricted three-body problem. pdf. Dynamics and Differential Equations, 17 (2005), 271-292.
- M. Conger and D. Viswanath, Riffle shuffles of decks with repeated cards. pdf. Annals of Probability, 34 (2006), 804-819.
- D. Viswanath, The fractal property of the Lorenz attractor. pdf. Physica D, 190 (2004), 115-128.
- D. Viswanath, Symbolic dynamics and periodic orbits of the Lorenz attractor. pdf. Nonlinearity, 16 (2003), 1035-1056.
- D. Viswanath, How many timesteps for a cycle? Analysis of the Wisdom-Holman algorithm? BIT, 42 (2002), 194-205.
- D. Viswanath, The Lindstedt-Poincaré technique as an algorithm for computing periodic orbits. pdf. SIAM Review, 43 (2001), 479-495.
- D. Viswanath, Global errors of numerical ODE solvers and Lyapunov’s theory of stability. pdf. IMA J. Numer. Anal., 21 (2001), 387-406.
- D. Viswanath, Random Fibonacci sequences and the number 1.13198824...pdf. Math. Comp., 69 (2000), 1131-1155.
- D. Viswanath and L.N. Trefethen, Condition numbers of random triangular matrices. pdf. SIAM J. Matrix. Anal. Appl., 19 (1998), 564-581.