Recent Papers and Preprints
  1.   Efstathios N. Antoniou, Adérito Araújo, Miguel D. Bustamante & Aviv Gibali, Physically Feasible Decomposition of Engino® Toy Models: A Graph Theoretic Approach, arXiv:1707.09040, 2017.

  2.   A. Araújo, S. Barbeiro, E. Cuesta & A. Durán, A discrete cross-diffusion model for image restoration, accepted for publication in Progress in Industrial Mathematics at ECMI 2016, Springer, ECMI book series of Mathematics in Industry.

  3.   A. Araújo, S. Barbeiro, & M. Khaksar Galati, Convergence of a leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials, accepted for publication in Progress in Industrial Mathematics at ECMI 2016, Springer, ECMI book series of Mathematics in Industry.

  4.   A. Araújo, S. Barbeiro, & M. Khaksar Galati, Stability of a leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials, Communications in Computational Physics 21(5) (2017), pp. 1350-1375. DOI: 10.4208/cicp.OA-2016-0110

  5.   A. Araújo, S. Barbeiro, E. Cuesta & A. Durán, Cross-diffusion systems for image processing: II. The nonlinear case, Journal of Mathematical Imaging and Vision, Volume 58, Issue 3, pp. 427-446, 2017. DOI:10.1007/s10851-017-0721-9.

  6.   A. Araújo, S. Barbeiro, E. Cuesta & A. Durán, Cross-diffusion systems for image processing: I. The linear case, Journal of Mathematical Imaging and Vision, Volume 58, Issue 3, pp. 447-467, 2017. DOI:10.1007/s10851-017-0720-x




Research Papers
  1.   M. Santos, A. Araújo, S. Barbeiro, F. Caramelo, A.L. Correia, M.I. Marques, L. Pinto, P. Serranho, R. Bernardes & M. Morgado, Simulation of Cellular Changes on Optical Coherence Tomography of Human Retina, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milan, August 2015, pp. 8147-8150. DOI: 10.1109/EMBC.2015.7320285.

  2.   M. Santos, A. Araújo, S. Barbeiro, F. Caramelo, A. Correia, M.I. Marques, M. Morgado, L. Pinto, P. Serranho & R. Bernardes, Maxwell's equations based 3D model of light scattering in the retina, IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), Porto, February 2015, pp. 1-5. DOI: 10.1109/ENBENG.2015.7088869

  3.   A. Araújo, S. Barbeiro & M. Khaksar Ghalati, A discontinuous Galerkin scheme for solving 2D wave propagation in anisotropic materials, IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), Porto, February, 2015, pp. 1-4. DOI: 10.1109/ENBENG.2015.7088866

  4.   A. Araújo, Amal 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. 48(4) (2015), pp. 045202 . DOI: 10.1088/1751-8113/48/4/045202

  5.   A. Araújo, Sílvia Barbeiro & Pedro Serranho, Convergence of finite difference schemes for nonlinear complex reaction-diffusion processes, SIAM J. Numer. Anal. 53(1) (2015), pp. 228-250. DOI:10.1137/130933642

  6.   A. Araújo, Sílvia Barbeiro & Pedro Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis 35(3) (2015), pp. 1381-1401. DOI: 10.1093/imanum/dru037.

  7.  A. Correia, L. Pinto, A. Araújo, S. Barbeiro, F. Caramelo, P. Menezes, M. Morgado, P. Serranho & R. Bernardes, Monte Carlo simulation of diabetic macular edema changes on optical coherence tomography data, 2014 IEEE-EMBS International Conference on Biomedical and Health Informatics (BHI), June 2014, pp. 724--727. DOI: 10.1109/BHI.2014.6864466

  8.  A. Correia, A. Araújo, S. Barbeiro, F. Caramelo, P. Serranho, M. Morgado & R. Bernardes, Simulation of DME changes on OCT, Acta Ophthalmologica, 92: 0 (2014). DOI: 10.1111/j.1755-3768.2014.2443.x

  9.   A. Araújo, 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, vol. 1, CMMSE 2014, Costa Ballena, Rota, Cádiz, Spain, 3-7 July, 2014, Jesús Vigo-Aguiar (Eds.), 2014, 88-99. ISBN: 978-84-616-9216-3

  10.   A. Araújo, C. Neves & E. Sousa, An alternating direction implicit method for a second-order hyperbolic diffusion equation with convection, Applied Mathematics and Computation, 239 (2014), pp. 17-28. DOI: 10.1016/j.amc.2014.04.044

  11.   A. Araújo, S. Barbeiro & J.A. Ferreira, Laboratory for Computational Mathematics: An Interface Between Academia and Industry, Alain Damlamian, José Francisco Rodrigues, Rudolf Strässer (Eds.): Educational Interfaces between Mathematics and Industry, New ICMI Study Series, Volume 16, 2013, pp 199-204. Springer 2013 ISBN 978-3-319-02269-7. DOI: 10.1007/978-3-319-02270-3_18

  12.   A. Araújo, A splitting algorithm for medical image denoising, Tuncer Ören, Janusz Kacprzyk, Leifur Þ. Leifsson, Mohammad S. Obaidat, Slawomir Koziel (Eds.): SIMULTECH 2013 - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications, Reykjavík, Iceland, 29-31 July, 2013, pp 704-709. SciTePress 2013 ISBN 978-989-8565-69-3

  13.   A. Araújo, S. Barbeiro, L. Pinto, F. Caramelo, A.L. Correia, M. Morgado, P. Serranho, A.S.C. Silva & R. Bernardes, Maxwell's equations to model electromagnetic wave's propagation through eye's structures, Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, vol. 1, CMMSE 2013, Almeria, Spain, 24­-27 June, 2013, Ian Hamilton & Jesús Vigo-Aguiar (Eds.), 2013, 121-129. ISBN: 978-84-616-2723-3

  14.   P. Rodrigues, P. Guimarães, A. Araújo, S. Barbeiro, R. Bernardes & P. Serranho, Explicit and Semi-Implicit Complex-Diffusion Schemes for Optical Coherence Tomography Despeckling, in Image Analysis and Recognition, ser. Lecture Notes in Computer Science, M. Kamel and A. Campilho, Eds. Springer Berlin Heidelberg, 2013, vol. 7950, pp. 282-289. DOI: 10.1007/978-3-642-39094-4_32

  15.   A. Araújo, A.K. Das, C. Neves & E. Sousa, Numerical solution for a non-Fickian diffusion in a periodic potential, Commun. Comput. Phys., 13 (2013), pp. 502-525. DOI: 10.4208/cicp.280711.010312a

  16.   A. Araújo, C. Neves & E. Sousa, A Laplace transform piecewise linearized method for a second order hyperbolic equation, CP1479, Numerical Analysis and Applied Mathematics, International Conference 2012, T. E. Simos, G. Psilioyios, and Cli. Tsitouras (Eds), 2012, American Institute of Physics, 2187-2190. DOI: 10.1063/1.4756626

  17.   A. Araújo, S. Barbeiro & P. Serranho, Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal. 50(3) (2012), 1284-1296. DOI: 10.1137/110825789

  18.   Pedro Serranho, Cristina Maduro, Torcato Santos, José Cunha-Vaz, Rui Bernardes, Adérito Araújo & Sílvia Barbeiro, Ocular fundus imaging: From structure to function, 1st Portuguese Meeting in Bioengineering (ENBENG), 2011. ENBENG 2011, IEEE, 2011, 1-4. DOI: 10.1109/ENBENG.2011.6026080

  19.   A. Araújo, Maria F. Patrício & José L. Santos, Optimal solution of a diffusive-reactive system with a control discrete source term, Int. J. Numer. Meth. Biomed. Engng., Vol 27, Issue 2, (2011), pages 186-197. DOI: 10.1002/cnm.1409

  20.   Rui Bernardes, Cristina Maduro, Pedro Serranho, Adérito Araújo, Sílvia Barbeiro, José Cunha-Vaz, Improved adaptive complex diffusion despeckling filter, Optics Express, Vol. 18, Issue 23, pp. 24048-24059, 2010.

  21.   A. Araújo, S. Barbeiro & J.A. Ferreira, Laboratory of Computational Mathematics: an interface between academia and industry, EIMI 2010 Conference Educational Interfaces Between Mathematics and Industry, A. Araújo, A. Fernandes, A. Azevedo & J.F. Rodrigues (Eds), 2010, COMAP, Bedford MA, USA, 75-84.

  22.   C. Neves, A. Araújo & E. Sousa, Numerical Approximation of a Transport Equation with a Time-Dependent Dispersion Flux, CP1048, Numerical Analysis and Applied Mathematics, International Conference 2008, T. E. Simos, G. Psilioyios, and Cli. Tsitouras (Eds), 2008, American Institute of Physics, 403-406.

  23.   A. Araújo, E. Sousa & A. Albuquerque Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a numerical solution, ANZIAM J., 50 (2008), C339-C353.

  24.   I.N. Figueiredo, P.N. Figueiredo, G. Stadler, O. Ghattas & A. Araújo, Variational image segmentation for endoscopic human colonic aberrant crypt foci, IEEE Transactions on Medical Imaging, vol. 29, no. 4, April 2010, 998-1011.

  25.   A. Araújo, Maria F. Patrício & José L. Santos, Optimal solution of a diffusion equation with a discrete source term, Int. J. Numer. Meth. Biomed. Engng. 2010; 26:1176-1187. DOI: 10.1002/cnm.1204

  26.   A. Araújo, D.M.G. Comissiong & G. Stadler, Numerical experiments for segmenting medical images using level sets, Computational Vision and Medical Image Processing, João Tavares & Natal Jorge (Eds), 2008, Taylor & Francis Group, London, 91-96 (DMUC report 06-51).

  27.   A. Araújo, J.R. Branco & J.A. Ferreira, On the stability of a class of splitting methods for integro-differential equations, Applied Numerical Mathematics 59 (2009), 436-453.

  28.   A. Araújo, J.A. Ferreira, N. Fernandes & P. de Oliveira, Using splitting methods in continuous digester modeling, Applied Mathematical Modelling, 32:9 (2008), 1869-1882.

  29.   A. Araújo & J. Oliveira, Envelope Transient Simulation of Nonlinear Electronic Circuits Using Multi-Rate Runge-Kutta Algorithms, WEAS Translations on Electronics, 3 (2006), 77-84.

  30.   A. Araújo, J.A. Ferreira & P. Oliveira, The effect of memory terms in diffusion phenomena, Journal of Computational Mathematics, 24 (2006), 91-102.

  31.   A. Araújo, J. Oliveira, Speed Versus Stability of Multi-Rate Runge-Kutta Methods in Transient Electronic Circuit Simulation, 4th WSEAS International Conference on System Science and Simulation in Engineering (ICOSSSE 05), Tenerife, Canary Islands, Spain, December 16-18, 2005, 90-93.

  32.   A. Araújo, J.A. Ferreira & P. Oliveira, Qualitative behaviour of numerical travelling solutions for reaction-diffusion equations with memory, Applicable Analysis, 84 (2005), 1231-1246.

  33.   A. Araújo, J.A. Ferreira & P. Oliveira, The role of abstract numerical properties in the change of character of reactive flows, Journal of Mathematical Fluid Mechanics, 7 (2005), 141-163.

  34.   A. Albuquerque, A. Araújo & E. Sousa, Application of the advection-dispersion equation to characterize the hydrodynamic regime in a submerged packed bed reactor, A. Tadeu and S.N. Atluri (eds.), In: Proceedings of the 2004 International Conference on Computational & Experimental Engineering & Sciences, pp. 548 - 553, (2004) Tech Science Press. (preprint 04-15, DMUC).

  35. A. Araújo, J.A. Ferreira, P. Oliveira, F. Patrício & P. Rosa, The use of splitting methods in the numerical simulation of reacting flows, Comput Visual Sci, 6 (2004), 59-66.

  36.   A. Araújo, A note on B-stability of splitting methods, Comput Visual Sci, 6 (2004), 53-57.

  37.   A. Araújo, J.A. Ferreira, N. Fernandes & P. de Oliveira, Simulation of the transient behaviour of a digester used in the pulp and paper industry, European Symposium on Computer-Aided Process Engineering - 14, A. Barbosa-Póvoa and H. Matos (Eds), 2004, Elsevier, 325-330.

  38.   A. Araújo, Additive methods for Hamiltonian partial differential equations, Second meeting on numerical methods for partial differential equations (Coimbra, 1998), 47-56, P. de Oliveira, F. Oliveira, F. Patrício, J.A. Ferrreira, A. Araújo eds., Department of Mathematics, University of Coimbra, 1999.

  39.   A. Araújo & A. Durán, Error propagation in the numerical integration of solitary waves. The regularized long wave equation, Appl. Numer. Math. 36 (2001), 197-217.

  40.   A. Araújo, J.M. Sanz-Serna, Symplectic additive Runge-Kutta methods for Hamiltonian systems, International Conference on Differential Equations (Lisboa, 1995), 239-246, Luís T. Magalhães, Carlos Rocha and Luís Sanches eds., World Scientific, Publishing, River Edge, NJ, 1998.

  41.   A. Araújo & A. Durán, Error growth in the numerical integration of the Benjamin-Bona-Mahoney equation, XVI CEDYA Congreso de Equaciones Diferenciales y Aplicaciones (Las Palmas de Gran Canaria, 1999), 899-906, R. Montenegro, G. Montero, G. Winter eds., Universidad de Las Palmas de Gran Canaria, 1999.

  42.   A. Araújo, A. Murua & J.M. Sanz-Serna, Symplectic methods based on decompositions, SIAM J. Numer. Anal. 34 (1997), 1926-1947.

  43.   A. Araújo & J.M. Sanz-Serna, Symplectic methods and NB-series, First meeting on numerical methods for partial differential equations, Textos de Matemática (Série B) 11, Departamento de Matemática, Coimbra (1995), 1-7.

  44.   A. Araújo & F. Aleixo Oliveira, Semi-discretization method for the heat equation with nonlocal boundary conditions, Communications in Numerical Methods in Engineering 10 (1994), 751-758.

  45.   A.L. Araújo, Métodos de semidiscretização para a equação de radiação, Actas do III Encontro de Mecânica Computacional 2 (1992), V1.1-V1.12.




Dissertations
  1.  Integradores Simplécticos Aditivos,
         Dissertação de Doutoramento, Universidade de Coimbra, 1998.

         English version: Additive Simplectic Integrators
         Ph. D. Thesis, University of Coimbra, 1998.

  2.  Métodos Numéricos para Equações Diferenciais,
         Dissertação de Mestrado, Universidade de Coimbra, 1993.

         English version: Numerical Methods for Differential Equations
         M. Sc. Thesis, University of Coimbra, 1993.


Books (edited)
  1.  Contas x Contos x Cantos e Que + Cumplicidades entre Literatura e Matemática (with A.P. Guimarães)
         Gradiva, 2012.

  2.  Educational Interfaces Between Mathematics and Industry (with A. Fernandes, A. Azevedo & J.F. Rodrigues)
         Proceedings of the EIMI 2010 Conference, COMAP, Bedford MA, USA, 2010.

  3.  Second Meeting on Numerical Methods for Differential Equations (with P. de Oliveira, F. Oliveira, F. Patrício, J. A. Ferreira)
         Proceedings of the Second Meeting on Numerical Methods for Differential Equations, Departamento de Matemática da Universidade de Coimbra, 1999.



Journals
  1.  CIM Bulletin
         (A. Araújo, A. Fernandes, S. Gama, editors, May 2011 to December 2015).

  2.   Gazeta de Matemática
         (vice-director, 2007-2010; director, October 2013 to present).



Course Notes
  1.   Matemática Computacional,
          Notas de curso, Universidade de Coimbra, 2013.
          (Primeira versão: Aulas de Análise Numérica, 2002).

  2.   Biomatemática,
          Notas de curso, Universidade de Coimbra, 2012.
          (Primeira versão: Aulas de Biomatemática, 2008).

  3.   Tratamento Matemático das Observações,
          Notas de curso, Universidade de Coimbra, 2003.
          (Primeira versão: Aulas de Tratamento Matemático das Observações, 2001).

  4.   Ajustamento de Curvas,
          Relatório de Aula, 1992.

  5.   Matemática do Discreto e do Contínuo,
          Texto de apoio a uma Acção de Formação FOCO, 1990.



Other
  1.   Increasing the Creativity of ENGINO Toy Sets and Generating Automatic Building Instructions (with A. Gibali, A. Kyprianou, E. Antoniou, M. D. Bustamante, Y. Kaminski & W. Okrasinski),
          125th European Study Group with Industry, Limassol, Cyprus, 2016.

  2.   Prediction model to textile parameters (with Eliana Silva, Isabel Cristina Lopes, A. Ismael F. Vaz & Rui Borges),
          Portuguese Study Groups' Reports, 119th European Study Group with Industry, Instituto Politécico do Porto, Porto, 2016.

  3.   Physical Model of MDF Boards (with A.R. Araújo, S. Clain, R. Costa, J.A. Ferreira, N. Peixinho, M. Peixoto & J. Sarmento),
          Portuguese Study Groups' Reports, 109th European Study Group with Industry, Universidade do Minho, Guimarães, 2015.

  4.   Optical modelling of the human retina (with S. Barbeiro),
          ECMI blog, April 7, 2015.

  5.   Packing and shipping cardboard tubes efficiently (with Isabel Cristina Lopes & Manuel Cruz),
          Portuguese Study Groups' Reports, 101st European Study Group with Industry, Universidade Nova de Lisboa, 2014.

  6.   Arte, literatura e matemática: cumplicidades de uma relação a três (with Carlos Augusto Ribeiro & Ana Paula Guimarães),
          Arte e Ciência em Diálogo, João Carlos Carvalho (org.), Grácio Editor, 2013, pp. 327-334. ISBN: 978-989-8377-51-0.

  7.   Modelling percolation and fractal structure in aerogels (with J. Correia, P. Freitas, M. Grinfeld & J. Pavlova),
          Portuguese Study Groups' Reports, 92nd European Study Group with Industry, ISEC, Coimbra, 2013.

  8.   Modelling drying process in paper manufacturing (with S. Abreu, S. Barbeiro, J. Correia, J.A. Ferreira, G. Pena, L. Morgado, J. Penedoones & F. Teodoro),
          Portuguese Study Groups' Reports, 86th European Study Group with Industry, ISEP, Porto, 2012.

  9.   Numerical approximation of a diffusive hyperbolic equation (with C. Neves & E. Sousa),
          DMUC report 09-02.

  10.   Através do espelho convexo,
          Via Latina, número 5, série 4, Março 2008, 73-76.

  11.   Aprender a brincar,
          Rua Larga, número 18, Outubro 2007, 17-18.

  12.   Le Programme MEF,
          Rapport de Stage, Université de Montpellier, 1990.