All Stories

  1. A CRITERION FOR ENSURING POSITIVITY OF FOURIER TRANSFORMS

    Article • Bulletin of the Australian Mathematical Society, August 2025, Cambridge University Press

    Professor Renato Spigler

  2. A Brief Survey on the Riemann Hypothesis and Some Attempts to Prove It

    Article • Symmetry, February 2025, MDPI AG

    Professor Renato Spigler

  3. A Short Survey on the Riemann Hypothesis and Some Attempts to Prove It

    Article • December 2024, MDPI AG

    Professor Renato Spigler

  4. High-frequency magnetohydrodynamics

    Article • Physics Letters A, September 2023, Elsevier

    Professor Renato Spigler

  5. Iterative Schemes for Probabilistic Domain Decomposition

    Article • SIAM Journal on Scientific Computing, August 2023, Society for Industrial & Applied Mathematics (SIAM)

    Professor Renato Spigler

  6. On the Relation between the Lifshitz--Slyozov and the Lifshitz--Slyozov--Wagner Models for Supersaturated Solutions

    Article • SIAM Journal on Applied Mathematics, January 2021, Society for Industrial & Applied Mathematics (SIAM)

    Professor Renato Spigler

  7. An ADI Method for the Numerical Solution of 3D Fractional Reaction-Diffusion Equations

    Article • Fractal and Fractional, December 2020, MDPI AG

    Professor Renato Spigler

  8. On the numerical solution of ill‐conditioned linear systems by regularization and iteration

    Article • Numerical Linear Algebra with Applications, September 2020, Wiley

    Professor Renato Spigler

  9. On a quantitative theory of limits: Estimating the speed of convergence

    Article • Fractional Calculus and Applied Analysis, August 2020, De Gruyter

    Professor Renato Spigler

  10. More around Cattaneo equation to describe heat transfer processes

    Article • Mathematical Methods in the Applied Sciences, March 2020, Wiley

    Professor Renato Spigler

  11. Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations

    Article • Advances in Difference Equations, August 2019, Springer Science + Business Media

    Professor Renato Spigler

  12. Geometric effects in the design of catalytic converters in car exhaust pipes

    Article • Mathematics-in-Industry Case Studies, August 2018, Springer Science + Business Media

    Professor Renato Spigler

  13. Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method

    Article • Journal of Mathematical Analysis and Applications, July 2018, Elsevier

    Professor Renato Spigler

  14. Fractional Dynamics

    Article • Fractal and Fractional, June 2018, MDPI AG

    Professor Renato Spigler

  15. Identifying the Fractional Orders in Anomalous Diffusion Models from Real Data

    Article • Fractal and Fractional, February 2018, MDPI AG

    Professor Renato Spigler

  16. How sharp is the Jensen inequality?

    Article • Journal of Inequalities and Applications, February 2015, Springer Science + Business Media

    Professor Renato Spigler

  17. Fractional oscillatory

    Article • Fractional Calculus and Applied Analysis, January 2015, De Gruyter

    Professor Renato Spigler, Moreno Concezzi

  18. Convergence of a family of neural network operators of the Kantorovich type

    Article • Journal of Approximation Theory, September 2014, Elsevier

    Professor Renato Spigler

  19. A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions

    Article • Journal of Integral Equations and Applications, March 2014, Rocky Mountain Mathematics Consortium

    Professor Renato Spigler

  20. On the interplay between asymptotic and numerical methods to solve differential equations problems

    Article • January 2014, ACM (Association for Computing Machinery)

    Professor Renato Spigler

  21. Multivariate neural network operators with sigmoidal activation functions

    Article • Neural Networks, December 2013, Elsevier

    Professor Renato Spigler

  22. Approximation by series of sigmoidal functions with applications to neural networks

    Article • Annali di Matematica Pura ed Applicata (1923 -), September 2013, Springer Science + Business Media

    Professor Renato Spigler

  23. Approximation results for neural network operators activated by sigmoidal functions

    Article • Neural Networks, August 2013, Elsevier

    Professor Renato Spigler

  24. Asymptotic-numerical solution of nonlinear systems of one-dimensional balance laws

    Article • Journal of Computational Physics, July 2013, Elsevier

    Professor Renato Spigler

  25. Solving Volterra integral equations of the second kind by sigmoidal functions approximation

    Article • Journal of Integral Equations and Applications, June 2013, Rocky Mountain Mathematics Consortium

    Professor Renato Spigler

  26. Random perturbations effects on the stability of Tension Leg Platforms in offshore engineering and of other large structures

    Article • Applied Mathematical Modelling, March 2013, Elsevier

    Professor Renato Spigler

  27. The “phase function” method to solve second-order asymptotically polynomial differential equations

    Article • Numerische Mathematik, December 2011, Springer Science + Business Media

    Professor Renato Spigler

  28. Singular perturbations of parabolic equations without boundary layers

    Article • Applicable Analysis, December 2011, Taylor & Francis

    Professor Renato Spigler

  29. Comparing Shannon to autocorrelation-based wavelets for solving singularly perturbed elliptic BV problems

    Article • BIT Numerical Mathematics, June 2011, Springer Science + Business Media

    Professor Renato Spigler

  30. Numerical treatment of degenerate diffusion equations via Feller's boundary classification, and applications

    Article • Numerical Methods for Partial Differential Equations, February 2011, Wiley

    Professor Renato Spigler

  31. Numerical solution of certain classes of transport equations in any dimension by Shannon sampling

    Article • Journal of Computational Physics, May 2010, Elsevier

    Professor Renato Spigler

  32. A fully scalable algorithm suited for petascale computing and beyond

    Article • Computer Science - Research and Development, April 2010, Springer Science + Business Media

    Professor Renato Spigler

  33. ERRATA: "NUMERICAL TREATMENT OF A NONLINEAR NONLOCAL TRANSPORT EQUATION MODELING CRYSTAL PRECIPITATION"

    Article • Mathematical Models and Methods in Applied Sciences, February 2010, World Scientific Pub Co Pte Lt

    Professor Renato Spigler

  34. Efficient Parallel Solution of Nonlinear Parabolic Partial Differential Equations by a Probabilistic Domain Decomposition

    Article • Journal of Scientific Computing, January 2010, Springer Science + Business Media

    Professor Renato Spigler

  35. On the Performance of a New Parallel Algorithm for Large-Scale Simulations of Nonlinear Partial Differential Equations

    Article • January 2010, Springer Science + Business Media

    Professor Renato Spigler

  36. A behavior-oriented model for long-term coastal profile evolution: Validation, identification, and prediction

    Article • Applied Mathematical Modelling, October 2009, Elsevier

    Professor Renato Spigler

  37. Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees

    Article • Journal of Computational Physics, August 2009, Elsevier

    Professor Renato Spigler

  38. NUMERICAL TREATMENT OF A NONLINEAR NONLOCAL TRANSPORT EQUATION MODELING CRYSTAL PRECIPITATION

    Article • Mathematical Models and Methods in Applied Sciences, September 2008, World Scientific Pub Co Pte Lt

    Professor Renato Spigler

  39. Asymptotic approximations for second-order linear difference equations in Banach algebras, II

    Article • Journal of Mathematical Analysis and Applications, April 2008, Elsevier

    Professor Renato Spigler

  40. Asymptotic approximations for second-order linear difference equations in Banach algebras, I

    Article • Journal of Mathematical Analysis and Applications, January 2008, Elsevier

    Professor Renato Spigler

  41. Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme

    Article • Physical Review E, September 2007, American Physical Society (APS)

    Professor Renato Spigler

  42. Supercomputing applications to the numerical modeling of industrial and applied mathematics problems

    Article • The Journal of Supercomputing, February 2007, Springer Science + Business Media

    Professor Renato Spigler

  43. Uniform and optimal estimates for solutions to singularly perturbed parabolic equations

    Article • Journal of Evolution Equations, February 2007, Springer Science + Business Media

    Professor Renato Spigler

  44. Liouville–Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations

    Article • Journal of Mathematical Analysis and Applications, January 2007, Elsevier

    Professor Renato Spigler

  45. Supremum principles for the higher-order derivatives of solutions to the Dirichlet problem for parabolic equations without compatibility conditions between the data

    Article • Journal of Differential Equations, November 2006, Elsevier

    Professor Renato Spigler

  46. Probabilistically induced domain decomposition methods for elliptic boundary-value problems

    Article • Journal of Computational Physics, December 2005, Elsevier

    Professor Renato Spigler

  47. Fast simulations of stochastic dynamical systems

    Article • Journal of Computational Physics, September 2005, Elsevier

    Professor Renato Spigler

  48. The Fractional Fourier Transform in the Analysis and Synthesis of Fiber Bragg Gratings

    Article • Opto-electronics, June 2005, Springer Science + Business Media

    Professor Renato Spigler

  49. The Kuramoto model: A simple paradigm for synchronization phenomena

    Article • Reviews of Modern Physics, April 2005, American Physical Society (APS)

    Professor Renato Spigler

  50. Domain Decomposition Solution of Elliptic Boundary-Value Problems via Monte Carlo and Quasi-Monte Carlo Methods

    Article • SIAM Journal on Scientific Computing, January 2005, Society for Industrial & Applied Mathematics (SIAM)

    Professor Renato Spigler

  51. Second Harmonics Effects in Random Duffing Oscillators

    Article • SIAM Journal on Applied Mathematics, January 2005, Society for Industrial & Applied Mathematics (SIAM)

    Professor Renato Spigler

  52. Validating the diffusion model for long-term coastal profile evolution

    Article • Journal of Inverse and Ill-Posed Problems, December 2004, De Gruyter

    Professor Renato Spigler

  53. Article • Siberian Mathematical Journal, January 2001, Springer Science + Business Media

    Professor Renato Spigler

  54. Article • Siberian Mathematical Journal, January 2001, Springer Science + Business Media

    Professor Renato Spigler

  55. Spectral analysis and computation for the Kuramoto-Sakaguchi integroparabolic equation

    Article • IMA Journal of Numerical Analysis, January 2001, Oxford University Press (OUP)

    Professor Renato Spigler

  56. Synchronization in populations of globally coupled oscillators with inertial effects

    Article • September 2000, American Physical Society (APS)

    Professor Renato Spigler

  57. Computing expansion coefficients in orthogonal bases of ultraspherical polynomials

    Article • Journal of Computational and Applied Mathematics, December 1994, Elsevier

    Professor Renato Spigler

  58. Cesaro′s Theorems for Complex Sequences

    Article • Journal of Mathematical Analysis and Applications, December 1993, Elsevier

    Professor Renato Spigler

  59. Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise

    Article • BIT Numerical Mathematics, December 1993, Springer Science + Business Media

    Professor Renato Spigler

  60. Abstract Versions of L′Hôpital′s Rule for Holomorphic Functions in the Framework of Complex B-Modules

    Article • Journal of Mathematical Analysis and Applications, November 1993, Elsevier

    Professor Renato Spigler

  61. Extending L′Hôpital′s Theorem to B-Modules

    Article • Journal of Mathematical Analysis and Applications, November 1993, Elsevier

    Professor Renato Spigler

  62. Asymptotic analysis and reaction-diffusion approximation forBGK kinetic models of chemical processes in multispecies gas mixtures

    Article • Zeitschrift für angewandte Mathematik und Physik, September 1993, Springer Science + Business Media

    Professor Renato Spigler

  63. A-stability of Runge-Kutta methods for systems with additive noise

    Article • BIT Numerical Mathematics, December 1992, Springer Science + Business Media

    Professor Renato Spigler

  64. WKBJ-type approximation for finite moments perturbations of the differential equation y″ = 0 and the analogous difference equation

    Article • Journal of Mathematical Analysis and Applications, September 1992, Elsevier

    Professor Renato Spigler

  65. Liouville-Green approximations for a class of linear oscillatory difference equations of the second order

    Article • Journal of Computational and Applied Mathematics, August 1992, Elsevier

    Professor Renato Spigler

  66. Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

    Article • Journal of Statistical Physics, April 1992, Springer Science + Business Media

    Professor Renato Spigler

  67. Improved estimates for the derivatives of the O-symbols in view of numerical applications

    Article • Journal of Mathematical Analysis and Applications, March 1992, Elsevier

    Professor Renato Spigler

  68. Reaction-diffusion models from the Fokker-Planck formulation ofchemical processes

    Article • IMA Journal of Applied Mathematics, January 1992, Oxford University Press (OUP)

    Professor Renato Spigler

  69. Numerical solution for the one-phase Stefan problem by Piecewise constant approximation of the interface

    Article • Computing, September 1990, Springer Science + Business Media

    Professor Renato Spigler

  70. Numerical simulation for degenerate diffusions

    Article • Applied Numerical Mathematics, July 1990, Elsevier

    Professor Renato Spigler

  71. Numerical simulation for certain stochastic ordinary differential equations

    Article • Journal of Computational Physics, January 1988, Elsevier

    Professor Renato Spigler

  72. Numerical treatment of a boundary-value problem for a certain singular parabolic partial differential equation

    Article • Journal of Computational Physics, January 1988, Elsevier

    Professor Renato Spigler

  73. Monte Carlo-type simulation for solving stochastic ordinary differential equations

    Article • Mathematics and Computers in Simulation, July 1987, Elsevier

    Professor Renato Spigler

  74. On the numerical solution of a nonlinear stochastic Helmholtz equation with a multigrid preconditioner

    Article • Applied Mathematics and Computation, July 1986, Elsevier

    Professor Renato Spigler

  75. Nonlinear parametric oscillations in certain stochastic systems: A random van der Pol oscillator

    Article • Journal of Statistical Physics, October 1985, Springer Science + Business Media

    Professor Renato Spigler

  76. The linear differential equation whose solutions are the products of solutions of two given differential equations

    Article • Journal of Mathematical Analysis and Applications, January 1984, Elsevier

    Professor Renato Spigler

  77. An application of group theory to matrices and to ordinary differential equations

    Article • Linear Algebra and its Applications, April 1982, Elsevier

    Professor Renato Spigler

  78. Scalability and Performance Analysis of a Probabilistic Domain Decomposition Method

    Article • Springer Science + Business Media

    Professor Renato Spigler