| Education |
BS in Pure Mathematics, University of Coimbra
DPhil in Numerical Analysis, University of Oxford
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Research Interests |
Fractional advection diffusion equation
Hyperbolic diffusion for transport problems
Convection diffusion equation
Stability analysis
Simulation of the Navier-Stokes equations
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Book |
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Finite Difference Methods for Fractional Diffusion Equations
Ercília Sousa, LNM 2389, Springer
Due: 14 January 2026
Research articles |
- C. Nhangumbe, E. Sousa, "Numerical solutions of an option pricing
rainfall weather derivatives model"
Comput. Math. Appl. Vol. 153 (2024) 43-55.
Full text (PDF)
- C. Jesus, E. Sousa, "High order numerical method for a subdiffusion problem"
Appl. Numer. Math. Vol. 205 (2024) 169-183.
Full text (PDF)
- E. Sousa, "Fractional diffusion problems with reflecting boundaries"
Lect. Notes Comput. Sc. 13952 (2024) pp. 164-171.
Full text (PDF)
- E. Sousa, "Convergence of consistent and inconsistent schemes
for
fractional diffusion problems with boundaries"
Adv. Comput. Math. Vol. 48 (2022) 68.
Full text (PDF)
- E. Sousa, "The convergence rate for difference approximations
to fractional boundary value problems"
J. Comput. Appl. Math. Vol. 415 (2022) 114486.
Full text (PDF)
- E. Sousa, "Consistency analysis of the Grunwald-Letnikov approximation
in
a bounded domain"
IMA J. Numer. Anal. Vol. 42 (2022) 2771-2793.
Full text (PDF)
- C. Jesus, E. Sousa, "Superdiffusion in the presence of a reflecting
boundary"
Appl. Math. Lett. Vol. 112 (2021) 106742.
Full text (PDF)
- C. Jesus, E. Sousa, "Numerical solutions for asymmetric Lévy flights"
Numer. Algor. Vol. 87 (2021) 967-999.
Full text (PDF)
- C. Jesus, E. Sousa, "Numerical method with fractional splines for a subdiffusion problem"
Bit Numer Math Vol. 60 (2020) 1075-1111.
Full text (PDF)
- L. Pinto, E. Sousa, "Positivity preserving schemes for the fractional
Klein-Kramers equation
with boundaries"
Commun. Nonlinear Sci. Numer. Simul. Vol. 91 (2020) 105444.
Full text (PDF)
2010 - 2019
- E. Sousa, A.K. Das, "A fractional diffusion model with resetting"
Lect. Notes Comput. Sc. 11386 (2019) pp. 509-516.
Full text (PDF)
- L. Pinto, E. Sousa, "Numerical solution of a time-space fractional
Fokker Planck equation
with variable force field and diffusion"
Commun. Nonlinear Sci. Numer. Simul. Vol. 50 (2017) pp. 211-228.
Full text (PDF)
- M. Nhangumbe, J. Gouveia, E. Sousa, M. Belbut, A. Mateus,
``Geometric study
of surface finishing
of selective laser melting moulds"
Procedia Manufacturing Vol. 12 (2017) pp. 174-182.
Full text (PDF)
- S.Gh. Bardeji, I.N. Figueiredo, E. Sousa, "Optical
flow with fractional order regularization:
Variational model and solution method"
Appl. Numer. Math. Vol. 114 (2017) pp. 188-200.
Full text (PDF)
- A. Araujo, A.K. Das, E. Sousa, "A numerical approach to study the Kramers equation for finite
geometries: boundary conditions and potential fields"
J. Phys. A: Math. Theor. Vol. 48 (2015) pp. 045202.
Full text (PDF)
- E. Sousa, Can Li, " A weighted finite difference method for the fractional
diffusion equation
based on the Riemann-Liouville derivative",
Appl. Numer. Math. Vol 90 (2015) pp. 22-37
Full text (PDF)
- S.Gh. Bardeji, I.N. Figueiredo, E. Sousa,
``Image contrast enhancement
using split Bregman method"
Computational Vision and Medical Image Processing V,
J. M. R.S. Tavares and R.M. Natal Jorge (eds), 63-68. CRC Press, 2016.
Full text (PDF)
- G. Gonçalves, N. Duro, E. Sousa, I. Figueiredo,
``Automatic extraction of tide-coordinated shoreline
using open source software
and land imagery",
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.
XL-7/W3, 953-957, 2015
Full text (PDF)
- E. Sousa, "An explicit high order method for fractional advection diffusion equations"
J. Comput. Phys. Vol. 278 (2014) pp. 257-274.
Full text (PDF)
- A. Araujo, C. Neves, E. Sousa, "An alternating direction implicit method
for a second-order hyperbolic diffusion equation with convection"
Appl. Math. Comput.
Vol. 239 (2014) pp. 17-28.
Full text (PDF)
- E. Sousa " A close look at fractional derivatives approximations",
Fractional Differentiation and Its Applications (ICFDA),
2014 International Conference on
IEEE Xplore
Abstract
Full text (PDF)
- G. Goncalves, N. Duro, E. Sousa, L. Pinto, I. Figueiredo,
" Detecting changes on coastal
primary sand dunes using multi-temporal Landsat imagery",
Proc. SPIE
Vol. 9244,
Image and Signal Processing for Remote
Sensing XX, 924420 (2014).
Full text (PDF)
- A Araujo, C. Neves, E. Sousa " A hybrid numerical method for a two-dimensional
second order
hyperbolic equation", Proceedings of the 14th International Conference
on Computational and
Mathematical Methods in Science and Engineering, CMMSE
2014, pp. 88-99.
Full text (PDF)
- E. Sousa, "Numerical solution of a model for turbulent diffusion"
Int. J. Bifurcation Chaos
Vol. 23 (10) (2013) pp. 1350166.
Full text (PDF)
- A. Araujo, A.K. Das, C. Neves, E. Sousa,
"Numerical solution for a
non-fickian diffusion
in a periodic potential"
Commun. Comput. Phys.
Vol. 13 (2) (2013) pp. 502-525.
Full text (PDF)
- E. Sousa " Super-diffusive transport processes in porous media",
Springer Proceedings in Mathematics and Statistics 28 (2013) pp.87-98.
Full text (PDF)
- E. Sousa, "A second order explicit finite difference method
for
the fractional advection diffusion equation",
Comput. Math. Appl. Vol. 64 (2012) pp. 3141-3152.
Full text (PDF)
- E. Sousa, "How to approximate the fractional derivative of
order 1 < α ≤ 2"
Int. J. Bifurcation Chaos
Vol. 22 (4) (2012) pp. 1250075.
Full text (PDF)
- A. Araujo, C. Neves, E. Sousa "A Laplace transform piecewise linearized
method
for a
second order hyperbolic equation",
Numerical Analysis and Applied Mathematics,
AIP Conference Proceedings 1479,
(2012) pp 2187-2190.
Full text (PDF)
- E. Sousa, " Numerical approximations for fractional diffusion equations via splines",
Comput. Math. Appl. Vol. 62 (2011) pp. 938-944.
Full text (PDF)
2001 - 2009
- E. Sousa, " Finite
difference approximations for a fractional advection diffusion problem",
J. Comput. Phys. Vol. 228 (2009) pp. 4038-4054.
Full text (PDF)
- E. Sousa, " Insights on a sign-preserving numerical method
for the
advection-diffusion equation",
Int. J. Numer. Methods Fluids
Vol. 61 (2009) pp. 864-887.
Full text (PDF)
- E. Sousa, " On the edge of stability analysis",
Appl. Numer. Math.
Vol. 59 (2009) pp. 1322 -1336.
Full text (PDF)
- A. Araujo, E. Sousa, A. Albuquerque " Longitudinal dispersion in a
horizontal
subsurface flow constructed wetland: a numerical solution",
ANZIAM J. Vol. 50, (2008) pp C339-C353.
Full text (PDF)
- C. Neves, A. Araujo, E. Sousa "Numerical approximation of a transport
equation
with a time-dependent dispersion flux",
Numerical Analysis and Applied Mathematics,
AIP Conference Proceedings 1048,
(2008) pp 403-406.
Full text (PDF)
- E. Sousa, "Higher order schemes and numerical boundary conditions",
Comput. Methods Appl. Mech. Eng. Vol. 196 (2007)
pp. 4444-4457
Full text (PDF)
- E. Sousa, "Development of finite difference schemes near an inflow
boundary",
Int. J. Numer. Methods Eng. Vol. 68 (2) (2006) pp. 210-230.
Full text (PDF)
- E. Sousa, " Stability
analysis of difference methods for parabolic initial value
problems"
J. Sci. Comput. Vol. 26 (1) (2006) pp. 45-66.
Full text (PDF)
- E. Sousa, I.J. Sobey, "Effect of boundary vorticity discretisation
on explicit stream-function vorticity calculations."
Int. J. Numer. Methods Fluids Vol. 49 (4) (2005)
pp. 371-393.
Full text (PDF)
- A. Albuquerque, A. Araujo, E. Sousa, "Application of the
advection-dispersion equation
to characterize the hydrodynamic regime
in a submerged packed bed reactor."
Advances in Computational & Experimental
Engineering & Science,
Tech Science Press, (2004) pp. 548-553.
Full text (PDF)
- E. Sousa, "The controversial stability analysis",
Appl. Math. Comput.
Vol. 145 (2003) pp. 777-794.
Full text (PDF)
- E. Sousa, I.J. Sobey, "Numerical stability of unsteady
stream-function vorticity calculations"
Commun. Numer. Methods Eng.
Vol. 19 (6) (2003) pp. 407-419
Full text (PDF)
- E. Sousa, I.J. Sobey,
"A family of finite difference schemes for the convection-diffusion
equation in two dimensions"
Numerical Mathematics and Advanced Applications,
Springer, (2003) pp. 179-188.
Full text (PDF)
- E. Sousa, I.J. Sobey, "On the influence of numerical
boundary conditions"
Appl. Numer. Math. Vol. 41 (2) (2002) pp. 325-344.
Full text (PDF)
- E. Sousa, "A Godunov-Ryabenkii instability for a
Quickest scheme"
Lect. Notes Comput. Sc. 1988 (2001) pp. 732-740.
Full text (PDF)
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