ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D. - T. Schwartzkopff; Claus-Dieter Munz; Eleuterio F. Toro (J. Sci. Comput., 2002)

ADER: Arbitrary High Order Godunov Approach. - Vladimir A. Titarev; Eleuterio F. Toro (J. Sci. Comput., 2002)

TVD Fluxes for the High-Order ADER Schemes. - Eleuterio F. Toro; Vladimir A. Titarev (J. Sci. Comput., 2005)

Derivative Riemann solvers for systems of conservation laws and ADER methods. - Eleuterio F. Toro; Vladimir A. Titarev (J. Comput. Phys., 2006)

MUSTA fluxes for systems of conservation laws. - Eleuterio F. Toro; Vladimir A. Titarev (J. Comput. Phys., 2006)

Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. - Michael Dumbser; Martin Käser; Vladimir A. Titarev; Eleuterio F. Toro (J. Comput. Phys., 2007)

Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. - Roberto Bernetti; Vladimir A. Titarev; Eleuterio F. Toro (J. Comput. Phys., 2008)

Solvers for the high-order Riemann problem for hyperbolic balance laws. - Cristóbal E. Castro; Eleuterio F. Toro (J. Comput. Phys., 2008)

A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. - Michael Dumbser; Dinshaw S. Balsara; Eleuterio F. Toro; Claus-Dieter Munz (J. Comput. Phys., 2008)

Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. - Michael Dumbser; Cedric Enaux; Eleuterio F. Toro (J. Comput. Phys., 2008)

ADER schemes for the shallow water equations in channel with irregular bottom elevation. - Gianluca Vignoli; Vladimir A. Titarev; Eleuterio F. Toro (J. Comput. Phys., 2008)

FORCE schemes on unstructured meshes I: Conservative hyperbolic systems. - Eleuterio F. Toro; Arturo Hidalgo; Michael Dumbser (J. Comput. Phys., 2009)

Upwind-biased FORCE schemes with applications to free-surface shallow flows. - Guglielmo Stecca; Annunziato Siviglia; Eleuterio F. Toro (J. Comput. Phys., 2010)

HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. - S. A. Tokareva; Eleuterio F. Toro (J. Comput. Phys., 2010)

Conservative Models and Numerical Methods for Compressible Two-Phase Flow. - Evgeniy I. Romenski; Dimitris Drikakis; Eleuterio F. Toro (J. Sci. Comput., 2010)

On some fast well-balanced first order solvers for nonconservative systems. - Manuel J. Castro; Alberto Pardo; Carlos Parés; Eleuterio F. Toro (Math. Comput., 2010)

High-order finite volume schemes for layered atmospheric models - Dante Kalise; Ivar Lie; Eleuterio F. Toro (CoRR, 2011)

A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems. - Michael Dumbser; Eleuterio F. Toro (J. Sci. Comput., 2011)

Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms. - Gino I. Montecinos; Cristóbal E. Castro; Michael Dumbser; Eleuterio F. Toro (J. Comput. Phys., 2012)

A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme. - Jun Bo Cheng; Eleuterio F. Toro; Song Jiang 004; Weijun Tang (J. Comput. Phys., 2013)

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state. - Bok Jik Lee; Eleuterio F. Toro; Cristóbal E. Castro; Nikolaos Nikiforakis 001 (J. Comput. Phys., 2013)

Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. - Lucas O. Müller; Carlos Parés; Eleuterio F. Toro (J. Comput. Phys., 2013)

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes. - Gino I. Montecinos; Lucas O. Müller; Eleuterio F. Toro (J. Comput. Phys., 2014)

Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes. - Gino I. Montecinos; Eleuterio F. Toro (J. Comput. Phys., 2014)

Advection-Diffusion-Reaction Equations: Hyperbolization and High-Order ADER Discretizations. - Eleuterio F. Toro; Gino I. Montecinos (SIAM J. Sci. Comput., 2014)

A novel numerical flux for the 3D Euler equations with general equation of state. - Eleuterio F. Toro; Cristóbal E. Castro; Bok Jik Lee (J. Comput. Phys., 2015)

Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws. - Eleuterio F. Toro; Gino I. Montecinos (J. Comput. Phys., 2015)

Brain venous haemodynamics, neurological diseases and mathematical modelling. A review. - Eleuterio F. Toro (Appl. Math. Comput., 2016)

Exploring various flux vector splittings for the magnetohydrodynamic system. - Dinshaw S. Balsara; Gino I. Montecinos; Eleuterio F. Toro (J. Comput. Phys., 2016)

Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations. - Saray Busto; Eleuterio F. Toro; M. Elena Vázquez-Cendón (J. Comput. Phys., 2016)

Junction-Generalized Riemann Problem for stiff hyperbolic balance laws in networks: An implicit solver and ADER schemes. - Christian Contarino; Eleuterio F. Toro; Gino I. Montecinos; Raul Borsche; Jochen Kall (J. Comput. Phys., 2016)

A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow. - S. A. Tokareva; Eleuterio F. Toro (J. Comput. Phys., 2016)

Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme. - Davide Vanzo; Annunziato Siviglia; Eleuterio F. Toro (J. Comput. Phys., 2016)

On the exact solution of the Riemann problem for blood flow in human veins, including collapse. - C. Spiller; Eleuterio F. Toro; M. Elena Vázquez-Cendón; Christian Contarino (Appl. Math. Comput., 2017)

A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system. - M. Strocchi; Christian Contarino; Q. Zhang; R. Bonmassari; Eleuterio F. Toro (Appl. Math. Comput., 2017)

A numerical method for junctions in networks of shallow-water channels. - Francesca Bellamoli; Lucas O. Müller; Eleuterio F. Toro (Appl. Math. Comput., 2018)

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows. - Saray Busto; Jose Luis Ferrín; Eleuterio F. Toro; M. Elena Vázquez-Cendón (J. Comput. Phys., 2018)

Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries. - Marco Petrella; S. A. Tokareva; Eleuterio F. Toro (J. Comput. Phys., 2019)

Bounds for Wave Speeds in the Riemann Problem: Direct Theoretical Estimates. - Eleuterio F. Toro; Lucas O. Müller; Annunziato Siviglia (CoRR, 2020)

A fully well-balanced scheme for the 1D blood flow equations with friction source term. - Beatrice Ghitti; Christophe Berthon; Minh Hoang Le; Eleuterio F. Toro (J. Comput. Phys., 2020)

Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form. - Eleuterio F. Toro; B. Saggiorato; Svetlana V. Tokareva; Arturo Hidalgo (J. Comput. Phys., 2020)

A splitting scheme for the coupled Saint-Venant-Exner model. - Annunziato Siviglia; Davide Vanzo; Eleuterio F. Toro (CoRR, 2021)

A flux-vector splitting scheme for the shallow water equations extended to high-order on unstructured meshes. - Eleuterio F. Toro; Cristóbal E. Castro; Davide Vanzo; Annunziato Siviglia (CoRR, 2021)

Total Effective Vascular Compliance of a Global Mathematical Model for the Cardiovascular System. - Morena Celant; Eleuterio F. Toro; Lucas O. Müller (Symmetry, 2021)

On well-posedness of a mathematical model for cerebrospinal fluid in the optic nerve sheath and the spinal subarachnoid space. - Alessia Scoz; Laura Bertazzi; Eleuterio F. Toro (Appl. Math. Comput., 2022)

Nonlinear lumped-parameter models for blood flow simulations in networks of vessels. - Beatrice Ghitti; Eleuterio F. Toro; Lucas O. Müller (CoRR, 2022)

Numerical approximation and uncertainty quantification for arterial blood flow models with viscoelasticity. - Christophe Chalons; Alessia Del Grosso; Eleuterio F. Toro (J. Comput. Phys., 2022)

ENO-ET: a reconstruction scheme based on extended ENO stencil and truncated highest-order term. - Gino I. Montecinos; Eleuterio F. Toro (Appl. Math. Comput., 2023)

High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties. - Ernesto Pimentel-García; Lucas O. Müller; Eleuterio F. Toro; Carlos Parés (J. Comput. Phys., 2023)

A semi-implicit finite volume scheme for blood flow in elastic and viscoelastic vessels. - Alessia Lucca; Saray Busto; Lucas O. Müller; Eleuterio F. Toro; Michael Dumbser (J. Comput. Phys., 2023)

Impact of Numerical Fluxes on High Order Semidiscrete WENO-DeC Finite Volume Schemes. - Lorenzo Micalizzi; Eleuterio F. Toro (CoRR, 2024)

Rusanov-type Schemes for Hyperbolic Equations: Wave-Speed Estimates, Monotonicity and Stability. - Eleuterio F. Toro; S. A. Tokareva (CoRR, 2024)

On simple well-balanced semi-implicit and explicit numerical methods for blood flow in networks of elastic vessels with applications to FFR prediction. - Alessia Lucca; Lucas O. Müller; Luigi Fraccarollo; Eleuterio F. Toro; Michael Dumbser (J. Comput. Phys., 2025)

Algorithms of very high space-time orders of accuracy for hyperbolic equations in the semidiscrete WENO-DeC framework. - Lorenzo Micalizzi; Eleuterio F. Toro (J. Comput. Phys., 2025)

High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics. - Shaoshuai Chu; Michael Herty; Eleuterio F. Toro (CoRR, 2025)