ORCID: http://orcid.org/0000-0002-5012-6061
SCOPUS: https://www.scopus.com/authid/detail.uri?authorId=7003624596
Numerical methods for ordinary and partial
differential equations, Computational finance, Differential Games.
Papers in refereed journals
J. de Frutos, B.
García-Archilla and J. Novo, Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives. J Sci Comput 103, 19 (2025). https://doi.org/10.1007/s10915-025-02833-0, https://rdcu.be/ebRfv
J. de Frutos, D. La
Torre, D. Luzzi. S. Marsiglio and G. Martín-Herrán,
“Balancing mitigation policies during pandemics: economic, health, and
environmental implications”, Annals of Operations Research, https://doi.org/10.1007/s10479-024-06083-5
J. de Frutos and J.
Novo, “Optimal bounds for numerical approximations of infinite horizon problems
based on dynamic programming approach”, SIAM Journal on Control and Optimization, 61
(2023), 415-433. https://doi.org/10.1137/21M1459290
J. de Frutos, V. Gatón, P.M: López-Pérez and G. Martín-Herrán,
“Investment in cleaner technologies in a transboundary pollution dynamic game.
A numerical investigation”, Dynamic Games And
Applications, 12, (2022), 813-843. https://doi.org/10.1007/s13235-022-00445-z. https://rdcu.be/cMgDh
J. de Frutos and V. Gatón,”A pseudospectral method
for Option Pricing with Transaction Costs under Exponential Utility”, Journal of Computational and Applied Mathematics, Volume 394, 1 October 2021, 113541, https://doi.org/10.1016/j.cam.2021.113541.
J. de Frutos, P.
López-Pérez and G. Martín-Herrán, “Equilibrium strategies in a multiregional
transboundary pollution differential game with spatially distributed
controls”, Automatica, 125, (2021), 109411, https://doi.org/10.1016/j.automatica.2020.109411.
J. de Frutos and G. Martín-Herrán, “Spatial effects and strategic behavior
in a multiregional
transboundary pollution dynamic game”. Journal of Environmental
Economics and Management, 97 (2019), 182-207, http://dx.doi.org/10.1016/j.jeem.2017.08.001.
J. de Frutos, B. García-Archilla and J. Novo, “Fully discrete approximations
to the time-dependent Navier-Stokes equations with a projection method in time
and grad-div stabilization”. Journal of Scientific Computing. 80 (2019),
1330-1368.
https://doi.org/10.1007/s10915-019-00980-9, https://rdcu.be/bEOKk.
J. de Frutos and G. Martín-Herrán, “Spatial vs. non-spatial
transboundary pollution control in a class of cooperative and non-cooperative
dynamic games”, European Journal of Operational Research 276 (2019), 379-394. https://doi.org/10.1016/j.ejor.2018.12.045
J. de Frutos, B. García-Archilla and J. Novo, “Grad-div stabilization
for the time-dependent Boussinesq equations with
inf-sup stable finite elements”, Applied Mathematics and Computation, 349 (2019), 281-291, https://doi.org/10.1016/j.amc.2018.12.062.
J. de Frutos and V. Gatón, “An extension of
Heston’s SV model to Stochastic Interest Rates”, Journal of Computational and
Applied Mathematics 354 (2019), 174-182, https://doi.org/10.1016/j.cam.2018.09.010.
J. de Frutos, B. García-Archilla, V. John and J. Novo,
“Error Analysis of Non Inf-sup Stable Discretizations
of the time-dependent Navier--Stokes Equations with Local Projection Stabilization”.
IMA Journal of Numerical Analysis 39 (2019), 1747-1786, https://doi.org/10.1093/imanum/dry044.
J. de Frutos and G. Martín-Herrán, “Selection of a Markov perfect Nash equilibrium
in a class of differential games”. Dynamic Games and Applications, 8
(2018), 620–636, https://doi.org/10.1007/s13235-018-0257-7, http://rdcu.be/JwcB
J. de Frutos, B.
García-Archilla, V. John and J. Novo, “Analysis of the grad-div stabilization for
the time-dependent Navier--Stokes equations with inf-sup stable finite
elements”. Advances in Computational Mathematics, 44 (2018), 195-225, http://dx.doi.org/10.1007/s10444-017-9540-1, http://rdcu.be/s1FU
J. de Frutos, B.
García-Archilla and J. Novo, “Error analysis of projection methods for non
inf-sup stable mixed finite elements. The Navier-Stokes equations’’. Journal of
Scientific Computing, 74 (2018), 426-455, http://dx.doi.org/10.1007/s10915-017-0446-3, http://rdcu.be/rSqO
J. de Frutos, B. García-Archilla and J. Novo,
“ Error analysis of projection methods for
non inf-sup stable mixed finite elements. The transient Stokes problem”. Appl.Math. Comput,
322 (2018), 154-173, https://doi.org/10.1016/j.amc.2017.11.046.
J. de Frutos and V. Gatón, “Chebyshev reduced basis function applied to option valuation”. Computational Management Science, 14 (2017), 465–491 http://dx.doi.org/10.1007/s10287-017-0287-4, http://rdcu.be/ucxb
J. de Frutos and V.
Gatón, “A spectral method for an optimal investment problem with transactions
costs and potential utility”. Journal of Computational and Applied Mathematics
Mathematics, 319 (2017), 262–276, http://dx.doi.org/10.1016/j.cam.2017.01.015.
J. de Frutos, B. García-Archilla, V. John and
J. Novo, “Grad-div stabilization for the evolutionary
Oseen problem with inf-sup stable finite elements”. J. Sci. Comput., 66, (2016),
991-1024. http://dx.doi.org/10.1007/s10915-015-0052-1.
J. de Frutos, V. John and J. Novo, “Projection methods for
incompressible flow problems with WENO finite difference schemes”, J. Comput. Phys., 309 (2016), 368–386. http://dx.doi.org/10.1016/j.jcp.2015.12.041.
J. de Frutos, B. García-Archilla and J. Novo, “Local error estimates for
the SUPG method applied to evolutionary convection-reaction-diffusion
equations”, J. Sci. Comput., 66 (2016), 528-554. http://dx.doi.org/10.1007/s10915-015-0035-2.
J. de Frutos and G.
Martín-Herrán, “Does Flexibility facilitate sustainability of cooperation over time? A
case study from environmental economics”, Journal of Optimization Theory and Applications,
165 (2015), 657-677. http://dx.doi.org/10.1007/s10957-014-0573-z.
J. de Frutos, B- García-Archilla, V. John and J. Novo, “An adaptive SUPG
method for evolutionary convection-diffusion equations”, Comput. Methods Appl. Mech. Engrg., 273 (2014),
219-237. http://dx.doi.org/10.1016/j.cma.2014.01.022
H. Ben-Ameur, J. de Frutos, T. Fakhfakh and V.
Diaby, “Upper and Lower Bounds for Convex Value
Functions of Derivative Contracts”, Economic Modelling, 34 (2013), 69-75. http://dx.doi.org/10.1016/j.econmod.2012.12.003
J. de Frutos, B. García-Archilla and J. Novo, “Static two-grid mixed finite-element approximations to the Navier-Stokes
equations ”, J. Sci. Comput., 52 (2012), 619-637. http://dx.doi.org/10.1007/s10915-011-9562-7
J. de Frutos, B. García-Archilla and J. Novo, “Optimal error bounds for two-grid schemes applied to the Navier-Stokes
equations ”, Appl. Math. Comput. 218, (2012), 7034-7051. http://dx.doi.org/10.1016/j.amc.2011.12.051
J. de Frutos, B. García-Archilla and J. Novo, “A posteriori error
estimation for mixed finite element approximations to the Navier-Stokes
equations”, J. Comput. Appl. Math.,
236 (2011),
1103-1122. http://dx.doi.org/10.1016/j.cam.2011.07.033
J. de Frutos, B. García-Archilla and J. Novo, “ Adaptive Finite Element Method for Evolutionary Convection
Dominated Problems”, Comput. Methods Appl. Mech. Engrg.,
200, (2011), 3601–3612. http://dx.doi.org/10.1016/j.cma.2011.08.010
J. de Frutos, B. García-Archilla and J. Novo, “Nonlinear convection-diffusion
problems: fully discrete approximations and a posteriori error estimates”, IMA
J. Numer. Anal., 31, (2011), 1402-1430. http://dx.doi.org/10.1093/imanum/drq017
J. de Frutos, B. García-Archilla and J. Novo, “Accurate approximations
to time-dependent nonlinear convection-diffusion problems”, IMA J. Numer.Anal., 30, (2010), 1137-1158. http://dx.doi.org/10.1093/imanum/drp007
M. Breton and J. de Frutos, “Option Pricing under GARCH Processes by PDE
Methods”, Operations Research, 58 (2010), 1148-1157. http://dx.doi.org/10.1287/opre.1100.0822
J. de Frutos, B. García-Archilla and J. Novo, “Stabilization of Galerkin finite element approximations to transient
advection-diffusion problems”, SIAM J. Numer. Anal.,
48 (2010), 953-979. http://dx.doi.org/10.1137/090763378
B. Bialecki and J. de Frutos, “ADI spectral
collocation methods for parabolic problems”, J. Comput. Phys., 229 (2010), 5182-5193. http://dx.doi.org/10.1016/j.jcp.2010.03.033
J. de Frutos, B. García-Archilla and J. Novo, “Postprocessing
Finite-Element Methods for the Navier-Stokes Equations: The Fully Discrete
Case”, SIAM J. Numer. Anal., 47 (2008), 596-621. http://dx.doi.org/10.1137/070707580
J. de Frutos and J. Novo, “Bubble stabilization of linear finite element
methods for Nonlinear evolutionary convection-diffusion equations”, Comput. Methods Appl. Mech. Engrg.,
198 (2008), 3988-3999. http://dx.doi.org/10.1016/j.cma.2008.03.028
J. de Frutos, “A Spectral Method for bonds”, Computers and Operations
Research, 35 (2008), 64-75.
http://dx.doi.org/10.1016/j.cor.2006.02.014
B. Ayuso, J. de Frutos and J. Novo, “Improving the accuracy of the
mini-element approximation to Navier-Stokes equations”, IMA J. Numer. Anal., 27 (2007), 198-218. http://dx.doi.org/10.1093/imanum/drl010
J. de Frutos, B. García-Archilla and J. Novo, “A posteriori error
estimates for fully discrete non-linear parabolic problems”, Comput. Methods Appl. Mech. Engrg.,
196 (2007), 3462-3474. http://dx.doi.org/10.1016/j.cma.2007.03.015
J. de Frutos, B. García-Archilla and J. Novo, “The Postprocessed Mixed
Finite-Element Method for the Navier-Stokes Equations: Refined Error Bounds”,
SIAM J. Numer. Anal., 46 (2007), 201-230. http://dx.doi.org/10.1137/06064458
J. de Frutos, “Implicit-explicit Runge-Kutta
methods for financial derivatives pricing models”, European Journal of
Operational Research, 171 (2006), 991-1004. http://dx.doi.org/10.1016/j.ejor.2005.01.013
J. de Frutos and J. Novo, “Element-wise a posteriori estimates based on hierarchical
bases for nonlinear parabolic problems”, Int. J. Num. Meth. Engr. 63 (2005),
1146-1173. http://dx.doi.org/10.1002/nme.1310
J. de Frutos and J.Novo, “A posteriori error
estimation with the $p$-version of the finite element method for nonlinear
parabolic differential equations”, Comput. Methods
Appl. Mech. Engrg., 191 (2002), 4893-4904.
http://dx.doi.org/10.1016/S0045-7825(02)00419-X
J. de Frutos and J. Novo, “Postprocessing the linear finite element
method”, SIAM J. Numer. Anal., 40 (2002), 805-819.
http://dx.doi.org/10.1137/S0036142900375438
M.P. Calvo, J. de Frutos and J. Novo, “Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations”,
App. Numer. Math., 37 (2001), 535-549. http://dx.doi.org/10.1016/S0168-9274(00)00061-1
J. de Frutos and J. Novo, “A spectral element method for the
Navier-Stokes equations with improved accuracy”, SIAM J. Numer.
Anal. 38 (2000), 799-819. http://dx.doi.org/10.1137/S0036142999351984
J. de Frutos, B. García-Archilla and J. Novo, “A Postprocessed Galerkin Method with Chebyshev or Legendre Polinomials”, Numer. Math. 86
(2000), 419-442. http://dx.doi.org/10.1007/s002110000188
J. de Frutos and R. Muñoz-Sola, “On Error estimates for Galerkin spectral discretizations
of parabolic problems with nonsmooth data”, Math. Comput. 70 (2001), 525-531. http://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01195-9/
J. de Frutos and J. Novo, “A postprocess based improvement of the
spectral element method”, Appl. Numer. Math. 33 (2000),
217-223. http://dx.doi.org/10.1016/S0168-9274(99)00086-0
J. de Frutos and J. Novo, “An enhanced pseudospectral Chebyshev method
for dissipative partial differential equations”, J. Comput. Appl. Math., 115 (2000), 137-150. http://dx.doi.org/10.1016/S0377-0427(99)00173-9
J. de Frutos and J.M. Sanz-Serna, “Accuracy and conservation properties
in numerical integration: the case of Korteweg-de
Vries equation”, Numer. Math. 75 (1997), 421-445. http://dx.doi.org/10.1007/s002110050247
J. de Frutos, M.A. López-Marcos and J.M. Sanz Serna, “A finite
difference scheme for the K(2,2) compacton
equation”, J. Comput. Phys. 120 (1995), 248-252. http://dx.doi.org/10.1006/jcph.1995.1161
B. García-Archilla and J. de Frutos, “Time integration of the non-linear
Galerkin method”, IMA J. Numer.
Anal. 15 (1995), 221-244.
http://dx.doi.org/10.1093/imanum/15.2.221
J. de Frutos and J.M. Sanz-Serna, “An easily implementable fourth-order method
for the time integration of wave problems”, J. Comput.
Phys. 103 (1992), 160-168. http://dx.doi.org/10.1016/0021-9991(92)90331-R
J. de Frutos, T. Ortega and J.M. Sanz-Serna, “Pseudospectral
method for the good Boussinesq equation”, Math. Comput. 57 (1991), 109-122. http://dx.doi.org/10.1016/0045-7825(90)90046-O
J. de Frutos, T. Ortega and J.M. Sanz-Serna, “A Hamiltonian, explicit
algorithm with spectral accurary for the `good' Boussinesq system”, Comp. Meth. Appl.
Mech. Engrg. 80 (1990),
417-423. http://dx.doi.org/10.1016/0045-7825(90)90046-O
J. de Frutos,
“Estabilidad y convergencia de esquemas numéricos para sistemas de Dirac no
lineales”, Met. Num. Cal. Dis. Ing. 5 (1989), 185-202. http://upcommons.upc.edu/handle/2099/8780
J. de Frutos and J.M. Sanz-Serna, “Split-step spectral schemes for
nonlinear Dirac systems”, J. Comput. Phys. 83 (1989), 407-423. http://dx.doi.org/10.1016/0021-9991(89)90127-7
Book Chapters
J. de Frutos and G. Martín-Herrán, “Non-linear incentive equilibrium
strategies for a transboundary pollution differential game”, in Games in
Management Science. Essays in honor of Georges Zaccour, pp. 187-204, Pierre-Olivier Pineau, Simon Sigué and Sihem Taboubi eds.,
Springer, 2020. https://link.springer.com/chapter/10.1007/978-3-030-19107-8_11
M. Breton and J. de Frutos, “Approximation of Dynamic Programs”, in Handbook of Computational Finance, pp.
633-649, Jin-Chuan Duan, James E.
Gentle, and Wolfgang Härdle(eds), Springer, 2012.
http://link.springer.com/chapter/10.1007/978-3-642-17254-0_23
J. de Frutos, B.
García-Archilla and J. Novo, “Numerical Experience with Transient
Convection–diffusion Problems: Adaptive Discretizations”,
in Adaptive Modelling and Simulation 2011, D. Aubry, P. Díez, B. Tie and N. Parés, eds., CIMNE, Barcelona,
2011, pp. 149-158. http://congress.cimne.com/admos2011/frontal/doc/ADMOS2011.pdf
J. de Frutos, B.
García-Archilla and J. Novo, "Efficient solution of Evolutionary Convection-Diffusion
Equations", In Adaptive Modelling and Simulation 2009, Ph. Bouillard and P. Díez es.,CIMNE, Barcelona, 2009, pp. 63-66.
J. de Frutos and J. Novo, “Stabilization and a posteriori error
estimation: nonlinear problems”, Adaptive Modeling
and Simulation 2007, 85-88, K. Runesson and P. Díez,
eds., CIMNE, Barcelona, 2007.
J. de Frutos, B. García-Archilla and J. Novo, “Adaptativity
and a posteriori error estimation for non-linear parabolic problems”, Adaptive Modeling and Simulation 2007, 81-84, K. Runesson
and P. Díez, eds., CIMNE, Barcelona, 2007.
J. de Frutos, “A finite element method for two factor convertible
bonds”, Numerical Methods in Finance, M. Breton and H. Ben_Ameur,
eds., 109-128, Springer, New-York, 2005.
M. P. Calvo, J. De Frutos and J. Novo, “An efficient way to avoid the
order reduction of linearly implicit Runge-Kutta
methods for nonlinear IBVP’s”, Mathematical Modelling, Simulation and
Optimization of Integrated Circuits, Vol. 146, 321-332, Birkhäuser
Verlag, Basel, 2003.
J. de Frutos and J. Novo, “A postprocessed Spectral Multidomain Method
for the Navier-Stokes Equations”, IMACS'98. Proceedings of Advances in
Scientific Computing Modelling, SK. Dey, J.P. Ziebarth
and J.M. Ferrándiz (eds.), Alicante 1998.
J. de Frutos and R. Muñoz-Sola, “Chebyshev pseudospectral
collocation for parabolic problems with nonconstant coefficients”, ICOSAHOM'95,
A.V. Illin and L.R. Scott (eds.), Houston Journal of
Mathematics, Houston 1996, 101-107.
https://www.math.uh.edu/~hjm/june1995/p00101-p00108.pdf
J. de Frutos and J.M. Sanz-Serna, “Erring and being Conservative”,
Numerical Analysis 1993. D.f. Griffiths and G.A.
Watson (eds.). Longman Scientific & Technical, Harlow Essex 1994, 75-88.
J. de Frutos and J.M. Sanz-Serna, “h-dependent stability thresholds
avoid the need for a priori bounds in nonlinear convergence proofs”,
Computational Mathematics III. S.O. Fatunla (ed.).
Ada Jane Press, Benin City 1994, 87-99.
J. de Frutos, T. Ortega and J.M. Sanz Serna “A Hamiltonian, explicit
algorithm with spectral accuracy for the ‘good’ Boussinesq
system”, Spectral and high order methods for partial differential
equations. C. Canuto and A. Quarteroni
(eds.). North Holland, Amsterdam 1990, 417-423.
Preprints
J. de Frutos,
V. Gatón, P. López and G. Martín-Herrán, “Investment in cleaner technologies in
a transboundary pollution dynamic game. A numerical investigation”, Les cahiers du
GERAD, G-2021-79, https://www.gerad.ca/en/papers/G-2021-79
J. de Frutos,
V. Gatón and J. Novo, “On Discrete-Time Approximations to Infinite Horizon
Differential Games”, https://arxiv.org/abs/2112.03153.
J. de Frutos
and J. Novo, “Optimal bounds for numerical approximations of infinite horizon
problems based on dynamic programming approach”, https://arxiv.org/abs/2111.07371.
J. de Frutos, P. López and G.Martín-Herrán, “Equilibrium strategies in a multiregional
transboundary pollution differential game with spatially distributed controls”,
Les Cahiers du GERAD
G-2019-86, https://www.gerad.ca/en/papers/G-2019-86
. http://arxiv.org/abs/1912.00481
J. de Frutos and G.
Martín-Herrán, “Spatial
vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative
dynamic games”, Les
Cahiers du GERAD G-2018-12, https://www.gerad.ca/en/papers/G-2018-12
.
J. de Frutos and G. Martín-Herrán, “Pollution
control in a multiregional setting: A differential game with spatially
distributed controls”, Gecomplexity Discussion
Papers, No. 1 (2016), January, 2016.
Title of the Project
Inversión en tecnologías limpias y políticas medioambientales:
Modelización matemática y análisis mediante juegos dinámicos VA169P20
Financial Support: Junta de Castilla y León (Supported by FEDER Funds) 264.000€
Period: November 1st 2020- October 31 2023.
Research leader: Javier de Frutos
Title of the Project: Modelización
matemática y análisis de regulaciones medioambientales, incentivos y uso
eficiente de energías limpias en un entorno dinámico VA024P17
Financial Support: Junta de Castilla y León (Supported by FEDER Funds) 120.000€
Period: July 26st 2017- October 31 2019.
Research leader: Javier de Frutos
Title of the project: Métodos numéricos para ecuaciones en dericadas
parciales dispativas: estabilización, adaptatividad y aplicaciones. MTM2016-78995-P
Financial Support: Agencia Estatal de
Investigación, MINECO, (Supported by FEDER Funds)
Period: December 31st 2016- December 3 2019.
Research leader: Julia Novo
Title
of the project:
The EU in the new economic complex geography: models, tools and policy
evaluation (GEOCOMPLEXITY). COST Action IS1104
Financial
Support: EU RTD
Framework Programme
Period: December March 22 2012- March 21 2016.
Research leader: Pasquale Commendatore