Artigos em Revistas Internacionais

• Lima, Pedro M.; Kherkouche, K.; Bellour, A. (2023)  Numerical solution of nonlinear third-kind Volterra integral equations using an iterative collocation method . International Journal of Computer Mathematics: 100, 2063-2076.

• Talaei, Y.; Lima, Pedro M. (2023)  An efficient spectral method for solving third-kind Volterra integral equations with non-smooth solutions . Computational and Applied Mathematics: 42, 193.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Sequential method for fast neural population activity reconstruction in the cortex from incomplete noisy measurements . Computers in Biology and Medicine: 141: 105103.

• Rouibah; Bellour, A.; Lima, Pedro M.; Rouibah; Bellour, A. (2022)  Iterative continuous collocation method for for solving nonlinear Volterra Integral Equations . Kragujevac Journal of Mathematics: 46, 635-648.

• Sequeira, T.; Lima, Pedro M. (2022)  Numerical Simulations of One- and Two-dimensional Stochastic Neural Field Equations with Delay . Journal of Computational Neuroscience: 50, 299-311.

• S. Bazm; Lima, Pedro M.; S. Nemati (2021)  Numerical solution of two-dimensional Volterra-Urysohn integral equations using Euler and trapezoidal discretization . Journal of Computational Mathematics: 398, 113628.

• Nemati, S.; Lima, Pedro M.; Torres, D. (2021)  Numerical solution of a class of third-kind Volterra Integral Equations using Jacobi wavelets . Numerical Algorithms: 86, 675-691.

• Nemati, S; Lima, Pedro M.; Torres, D. (2021)  Numerical solution of variable-order fractional differential equations using Bernoulli polynomials . Fractal and Fractional: 5, 219.

• Kulikov, Gennady Yu; Lima, Pedro M.; Kulikova, Maria (2021)  Numerical solution of the neural field equation in the presence of random disturbance. . Journal of Computational and Applied Mathematics: 387: 112563.

• Khercouche, K.; Lima, Pedro M.; Bellour, A. (2021)  Iterative collocation method for solving a class of nonlinear weakly singular Volterra integral equations . Dolomites Research Notes on Approximation: 14, 33-41.

• Sabermahani, S.; Ordokhani, Y.; Lima, Pedro M. (2020)  A novel Lagrange operational matrix and tau-collocation method for solving variable-order fractional differential equations . Iranian Journal of Science and Technology, Transactions A: 44, 127-135.

• Nemati, S.; Lima, Pedro M.; Sedaghat,S (2020)  Legendre wavelet collocation method combined with the Gauss–Jacobi quadrature for solving fractional delay-type integro-differential equations . Applied Numerical Mathematics: 149, 99-112.

• Rahimkani,P.; Ordokhani, Y; Lima, Pedro M. (2019)  An improved composite collocation method for distributed-order fractional differential equations based on fractional Chelyshkov wavelets . Applied Numerical Mathematics: 145, 1-27.

• Nemati, S.; Lima, Pedro M.; Torres, Delfim (2019)  A numerical approach for solving fractional optimal control problems using modified hat functios . Communications in Nonlinear Science and Numerical Simulations: 78, 104849.

• Lima, Pedro M.; S. Nemati (2018)  Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions . Applied Mathematics and Computation: 327, 79-92.

• Lima, Pedro M.; S. Sedaghat; S. Nemati (2018)  An effective numerical method for solving fractional pantograph differential equations using modification of hat functions, . Applied Numerical Mathematics: 131, 174-189.

• Lima, Pedro M.; Bulatov, M.V.; Bellours, A. (2018)  Numerical solution of integro-differential equations arising from singular boundary value problems . Applied Mathematics and Computation: 336, 1-15.

• Lima, Pedro M.; Morgado, M. Luísa; Schöbinger, M. ; Weinmüller, E.B. (2017)  A Novel computational approach to singular free boundary problems in ordinary differential equations . Applied Numerical Mathematics: 114, 97-107.

• Diogo, Teresa; Lima, Pedro M.; Pedas, Arvet; Vainikko,Gennadi (2017)  Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations . Applied Numerical Mathematics: 114, 63–76.

• Ford, N.J.; Lima, Pedro M.; Lumb, P.M. (2017)  Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh–Nagumo equation . Applied Mathematics and Computation: 293, 448-460.

• Graça, M.M. ; Lima, Pedro M. (2016)  On High Order Barycentric Root-Finding Methods . Tendências em Matemática Aplicada e Computacional: 17(3), 321-330.

• Lima, Pedro M.; Buckwar, E. (2015)  Numerical solution of the neural field equation in the two-dimensional case . SIAM Journal o Scientific Computing: 37, B962-B979.

• Graca, M.M.; Lima, Pedro M. (2015)  Root finding by high order iterative methods based on quadratures . Applied Mathematics and Computation: 264, 466-482.

• Lima, Pedro M.; E. Buckwar (2015)  Numerical solution of the neural field equation in the two-dimensional case . SIAM Journal of Scientific Computing: 37, B962- B979.

• Bulatov, M.; Lima, Pedro M.; Than, Do Tien (2015)  An integral method for the numerical solution of nonlinear singular boundary value problems . Bulletin of the South Ural State University, Ser. Mathematical Modelling, Programming & Computer Software: 8, 5-13.

• Kulikov, Gennady Yu; Lima, Pedro M.; Morgado, M. Luísa (2014)  Analysis and Numerical Approximation of Singular Boundary Value Problems with the P-Laplacian in Fluid Mechanics . Journal of Computational and Applied Mathematics: 262, 87-104.

• Bulatov, Mikhail V.; Lima, Pedro M.; Weinmüller, Ewa B.  (2014)  Existence and uniqueness of solutions to weakly singular integral-algebraic and integro differential equations . Central European Journal of Mathematics: 12(2), 308-321.

• Lima, Pedro M.; Ford, Neville J.; Lumb, Patricia M. (2014)  Computational Methods for a Mathematical Model of Propagation of Nerve Impulses in Myelinated Axons . Applied Numerical Mathematics: 85, 38-53.

• Hastermann, G.; Lima, Pedro M.; Morgado, M. Luísa; Weinmüller, E.B. (2013)  Density profile equation with p-Laplacian: analysis and numerical simulation . Applied Mathematics and Computation: 225, 550-561.

• Morgado, M. Luísa; Ford, N. J.; Lima, Pedro M. (2013)  Analysis and Numerical Methods for Fractional Differential Equations with Delay . Journal of Computational and Applied Mathematics: 252, 159-168.

• Lima, Pedro M.; Nemati, S.; Ordokhani, Y. (2013)  Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials . Journal of Computational and Applied Mathematics: 242, 53-69.

• Lima, Pedro M.; Morgado, M. Luísa (2012)  Efficient computational methods for singular free boundary problems using smoothing variable substitutions . Journal of Computational and Applied Mathematics: 236(12), 2981-2989.

• Bulatov, M.V. ; Lima, Pedro M. (2011)  Two-dimensional integral-algebraic systems: analysis and computational methods . Journal of Computational and Applied Mathematics: 236(12), 132-140.

• Babolian, E.; Bazm, S.; Lima, Pedro M. (2011)  Numerical Solution of Nonlinear Two-Dimensional Integral Equations Using Rationalized Haar Functions . Communications in Nonlinear Science and Numerical Simulation: 16(3), 1164-1175.

• Lima, Pedro M.; Teodoro, Filomena; Ford, Neville J.; Lumb, Patricia M. (2010)  Analytical and Numerical Investigation of Mixed-Type Functional Differential Equations . Journal of Computational and Applied Mathematics: 234(9), 2826-2837.

• Lima, Pedro M.; Morgado, M. Luísa (2010)  Numerical Modelling of Oxygen Diffusion in Cells with Michaelis-Menten Uptake Kinetics . Journal of Mathematical Chemistry: 48(1), 145-158.

• Morgado, M. Luísa; Lima, Pedro M. (2010)  Finite Difference Solution of a Singular Boundary Value Problem for the P-Laplace Operator . Numerical Algorithms: 55(2-3), 337-348.

• Morgado, M. Luísa; Lima, Pedro M. (2010)  Numerical Solution of a Class of Singular Free Boundary Problems Involving the M-Laplace Operator . Journal of Computational and Applied Mathematics: 234(9), 2838-2847.

• Ford, Neville J.; Lumb, Patricia M.; Lima, Pedro M.; Teodoro, Filomena (2010)  The Numerical Solution of Forward-Backward Differential Equations: Decomposition and Related Issues . Journal of Computational and Applied Mathematics: 234(9), 2745-2756.

• Lima, Pedro M.; Teodoro, Filomena; Ford, Neville J.; Lumb, Patricia M. (2010)  Finite Element Solution of a Linear Mixed-Type Functional Differential Equation . Numerical Algorithms: 55(2-3), 301-320.

• Lima, Pedro M.; Morgado, M. Luísa (2009)  Analytical-numerical investigation of a singular boundary value problem for a generalized Emden–Fowler equation . Journal of Computational and Applied Mathematics: 229(2), 480-487.

• Teodoro, Filomena; Lima, Pedro M.; Ford, Neville J.; Lumb, Patricia M. (2009)  New Approach to the Numerical Solution of Forward-Backward Equations . Frontiers of Mathematics in China: 4(1), 155-168.

• Teodoro, Filomena; Lima, Pedro M.; Ford, N.; Lumb, P. (2009)  New approach to the numerical solution of forward-backward equations . Frontiers of Mathematics in China: 4(1), 155-168.

• Konyukhova, N.B.; Lima, Pedro M.; Morgado, M. Luísa; Soloviev, M.B. (2008)  Bubbles and droplets in nonlinear physics models: analysis and numerical simulation of singular nonlinear boundary value problems . Computational Mathematics and Mathematical Physics: 48(11), 2018-2058.

• Diogo, Teresa; Lima, Pedro M. (2008)  Superconvergence of collocation methods for a class of weakly singular Volterra integral equations . Journal of Computational and Applied Mathematics: 218, 307-316.

• Diogo, Teresa; Ford, N.J; Lima, Pedro M.; Thomas, S. (2007)  Solution of a singular integral equation by a split- interval method . International Journal of Numerical Analysis and Modeling: (167)4, 63-73.

• Ford, NJ; Diogo, Teresa; Lima, Pedro M.; Thomas, S. (2007)  Numerical modelling of qualitative behaviour of solutions to convolution integral equations . J. Computational and Applied Mathematics: 205, 849 – 858..

• Diogo, Teresa; Lima, Pedro M. (2007)  Collocation solutions of a weakly singular Volterra integral equation . Tendências da Matemática Aplicada e Computacional (TEMA ): 8, 229-238.

• Kitzhofer, G.; Koch, O.; Lima, Pedro M.; Weinmueller, E. (2007)  Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics . Journal of Scientific Computing: 32(3), 411-424.

• Diogo, Teresa; Lima, Pedro M.; Rebelo, M (2006)  Numerical Solution of a Nonlinear Abel Type Volterra Integral Equation . Communications on Pure and Applied Analysis: 5(2), 277-288.

• Diogo, Teresa; Lima, Pedro M.; Ford, Neville J.; Valtchev, Svilen S.  (2006)  Numerical Methods for a Volterra Integral Equation with Non-smooth Solutions . Journal of Computational and Applied Mathematics: 189(1-2), 412–423.

• Lima, Pedro M.; Morgado, M. Luísa (2006)  Analysis of Singular Boundary Value Problems for an Emden-Fowler Equation . Communications on Pure and Applied Analysis: 5(2), 321-336.

• Diogo, Teresa; Franco, NB; Lima, Pedro M. (2004)  High order product integration methods for a Volterra integral equation with logarithmic singular kernel . Communications on Pure and Applied Analysis: 3, 217--235.

• Lima, Pedro M.; Diogo, Teresa (2002)  Numerical solution of a non-uniquely solvable Volterra integral equation using extrapolation methods . J. Computational and Applied Mathematics: 140, 537--557.

• Diogo, Teresa; Franco, NB; Lima, Pedro M. (2000)  Analysis of product integration methods for a class of singular Volterra integral equations . Tendências da Matemática Aplicada e Computacional (TEMA ): 1(2), 373--387.

• Lima, Pedro M.; Diogo, Teresa (1997)  An extrapolation method for a Volterra integral equation with weakly singular kernel, . Applied Numerical Mathematics: 24, 131--148.

Artigos ou Capítulos em Livros Editados

• Morgado, M. Luísa; Lima, Pedro M.; M. V. Mendes (2020)  Numerical Solution of the Time Fractional Cable Equation . Dierential and Dierence Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, Springer, Cham.: vol 333.

• Lima, Pedro M. (2019)  Numerical Investigation of Stochastic Neural Field Equations . Advances in Mathematical Methods and High Performance Computing: Springer, 51-67.

• Lima, Pedro M.; E. Buckwar (2017)  Computational Methods for Two-Dimensional Neural Fields . Nonlinearity: Problems, Solutions and Applications: Nova Science Pub., New York, 3-32.

• Diogo, Teresa; Ford, N.; Jackiewicz, Z.; Lima, Pedro M.; Morgado, M. Luísa; Rebelo, Magda (2016)  The Fifth International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP 2015) . Applied Numerical Mathematics, October 22–24, 2015, Lagos, Algarve, Portugal: 114.

• Pedro, A.; Lima, Pedro M. (2013)  Existence of nonoscillatory solutions of the discrete FitzHugh-Nagumo S system . Differential and Difference Equations with Applications, Springer Proceedings in Mathematics & Statistics, Springer, New York: 47, 551-560.

• Lima, Pedro M.; Teodoro, Filomena; Ford, N. J.; Lumb, P. M. (2013)  Analysis and computational approximation of a forward-backward equation arising in nerve conduction . Differential and Difference Equations with Applications, Springer Proceedings in Mathematics & Statistics, Springer, New York: 47, 475-483.

• Diogo, Teresa; Kolk,M; Lima, Pedro M.; Pedas,A (2010)  High order methods for weakly singular Volterra integro-differential equations . Integral Methods in Science and Engineering, Birkhäuser Boston: 2, 151-160.

• Diogo, Teresa; Lima, Pedro M.; Rebelo, Magda (2010)  Extrapolation Methods for a Nonlinear Weakly Singular Volterra Integral Equation . Proceedings of International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), 19–25 September 2010, Rhodes, Greece: 1281, 1175-1178.

Comunicações em Actas de Conferência

• Sequeira, T.; Lima, Pedro M. (2023)  Numerical Simulation of the Stochastic Neural Field Equation with Delay . Proceedings of the Second International Conference in Biomathematics , Univerity of Mazandaran, Iran, 488-495.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Pattern Recognition Facilities of Extended Kallman Filtering in Stochastic Neural Fields . Proceedings of ECC2022, 1436-1441.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Accurate Ito-Taylor-Discretization-Based State Estimation in Stochastic Neural Field Equations with Infinte Signal Transmissiion Rate . Proceedings of ECC2022, 1436-1441.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2021)  Reconstruction of hidden states in stochastic neural field equations with infinite signal transmission rate . Proceedings of the 25th International Conference on System Theory, Control and Computing, Iasi, Romania, 358-365.

• Lima, Pedro M.; Erlhagen, W.; Kulikov, Gennady Yu; Kulikova, Maria (2021)  Mathematical modeling of working memory in the presence of random disturbance using neural field equations . Proceedings of V International Conference "Modeling of Nonlinear Processes and Systems" (MNPS-2020). EPJ Web of Conferences: 248, 01021.

• Kulikova, Maria; Kulikov, Gennady Yu; Lima, Pedro M. (2020)  Accuracy study in numerical simulations to stochastic neural field equations . Proceedings of the 24th International Conference on System Theory, Control and Computing, Sinaia, Romania, 254-261.

• Kulikova, Maria; Kulikov, Gennady Yu; Lima, Pedro M. (2019)  Effective Numerical Solution to Two-Dimensional Stochastic Neural Field Equations. . Proceedings of the 23rd International Conference on System Theory, Control and Computing, 650-655.

• Kulikov, Gennady Yu; Kulikova, Maria; Lima, Pedro M. (2019)  Numerical Simulation of Neural Fields with Finite Transmission Speed and Random Disturbance . Proceedings of the 23rd International Conference on System Theory,, 644-649.

• Lima, Pedro M.; Nemati,S (2018)  Numerical Solution of a Third-Kind Volterra Integral Equation Using an Operational Matrix Technique . 2018 European Control Conference, ECC 2018, 8550223, 3215-3220.

• Lima, Pedro M.; Erlhagen, W. (2018)  Numerical Simulations of Two-Dimensional Neural Fields with Applications to Working Memory . 2018 European Control Conference, ECC 2018, 8550211, 2040-2045.

• Nemati, S.; Lima, Pedro M.; Ordokhani, Y. (2015)  Numerical Method for the Mixed Volterra-Fredholm Integral Equation Using Hybrid Legendre Functions . Conference Applications of Mathematics 2015, 186-195.

• Lima, Pedro M.; Buckwar, E. (2015)  Numerical Investigation of the Two-dimensional Neural Field Equation with Delay . 2015 Second International Conference on Mathematics and Computers in Sciences and in Industry (MCSI), IEEE Conference Publications, 131-137.

• Lima, Pedro M.; Buckwar, E. (2015)  Numerical Simulations in Two-Dimensional Neural Fields . BMC Neuroscience.

• Ford, N.J.; Lima, Pedro M.; Lumb, P.M.  (2015)  Mathematical Modelling and Numerical Simulations in Nerve Conduction . Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - BIOSIGNAL 2015, 283-288.

• Morgado, M. Luísa; Ford, N. J.; Lima, Pedro M. (2011)  Analysis of linear delay fractional differential initial value problems . Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2011): Vol. III, 878-885.

• Morgado, M. Luísa; Lima, Pedro M. (2010)  Finite difference schemes for singular free boundary problems . Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010: Vol. II, 667-676.

• Morgado, M. Luísa; Lima, Pedro M. (2009)  Numerical methods for a singular boundary value problem with application to a heat conduction model in the human head . Proceedings of the 9th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2009): Vol. III, 755-764.

• Lima, Pedro M.; Morgado, M. Luísa (2009)  Numerical methods for singular boundary value problems involving the p-Laplacian . Proceedings of International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine, AIP Conference Proceedings: 1124(1), 214-223.

• Konyukhova, N. B.; Lima, Pedro M.; Morgado, M. Luísa; Soloviev, M. B.  (2007)  Singular Nonlinear Boundary Value Problem for the Bubble-type or Droplet-type Solutions in Nonlinear Physics Models . Spectral and Evolution problems, Proceedings of the XVIII Crimean Autumn Mathematical School-Symposium: Vol. 18, 160-170.

• Lima, Pedro M.; Morgado, M. Luísa (2007)  Analysis and numerical approximation of a singular boundary value problem for the one-dimensional p-laplacian . Proceedings of the 4th WSEAS International Conference on Fluid Mechanics, 42-47.

• Lima, Pedro M.; Morgado, M. Luísa (2005)  Numerical approximation of singular boundary value problems for a nonlinear differential equation . Proceedings of the 11th International Conference on Differential Equations and Their Applications (Equadiff11), 201-211.

• Diogo, Teresa; Lima, Pedro M.; Rebelo, Magda (2005)  Computational methods for a nonlinear Volterra integral equation . Proceedings of the 7th Hellenic European Conference on Computer Mathematics and its Applications (HERCMA 2005), Athens, 22-24 September 2005, HERCMA Conference Series, LEA Publishers, ISBN: 960-87275-8-8, 100-107.

• Diogo, Teresa; Valtchev, Svilen S. ; Lima, Pedro M. (2003)  Numerical solution of a singular Volterra integral equation by piecewise polynomial collocation . Proceedings of the IXth International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC IX).

• Diogo, Teresa; Lima, Pedro M.; Valtchev, Svilen S.  (2003)  Numerical methods for a non-uniquely solvable Volterra integral equation . Proceedings of the XXIVth Iberian Latin-American Congress on Computational Methods in Engineering (XXIV CILAMCE).

• Diogo, Teresa; Lima, Pedro M. (2002)  A comparative study of numerical methods for a certain Volterra integral equation with weakly singular kernel . Proc. of the 5th Hellenic-European Research on Computer Mathematics and its Applications (HERCMA 2001), 20-22 Setember 2001, Athenas, Greece, E. A. Lipitakis (Ed.), 574-582.

• Diogo, Teresa; Lima, Pedro M. (2000)  Numerical solution of a non-uniquely solvable Volterra integral equation . In:Finite difference schemes: theory and applications, R.Ciegis, A.Samarskii and M.Sapagovas (Eds.).

Edição de Livros

• Diogo, Teresa; Neville Ford; Zdzislaw Jackiewicz; Lima, Pedro M.; Morgado, M. Luísa; Rebelo, Magda (2017)  Special issue:Selected papers presented at IWANASP15, October 22-24, 2015, Lagos, Algarve, Portugal . Applied Numerical Mathematics: 114, 1-222.

• Baker, Christopher T. H.; Ford, Neville J.; Diogo, Teresa; Lima, Pedro M.; Sequeira, Adélia (2010)  Special issue: Third International Workshop on Analysis and Numerical Approximation of Singular Problems . Journal of Computational and Applied Mathematics: 234(9), 2617.

• Baker, C.; Diogo, Teresa; Flessas, G.; Lima, Pedro M.; Makroglou, A.; Shen, J. (2009)  [Special issue: analysis and numerical approximation of singular problems- Selected papers of IWANASP06, Samos, Greece, September 6-8, 2006 . Journal of Computational and Applied Mathematics: 229 (2).

• Diogo, Teresa; Lima, Pedro M.; Tang,T. (2006)  Selected papers based on the presentations at the International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP04), Lisbon, Portugal, November 10--12, 2004. . Communications on Pure and Applied Analysis: vol.5(2).

Artigos em Revistas Científicas Nacionais

• Graça, M.M.; Lima, Pedro M. (2014)  Funcoes iteradoras de ordem de convergencia superior do metodo de Newton . Boletim da Sociedade Portuguesa de Matematica, (in press).

• Investigador Responsável do Projecto POCTI/MAT/45700/2002,  2003-2006. 'Métodos computacionais para problemas singulares', financiado pela FCT
  

•  Coordenador da equipa portuguesa do projecto B-15/08 das Acções Integradas Luso-Britânicas,   2008-2009,  'Quality assurance of computer simulatons of certain systems in the environmental and medical sciences'. 

• Membro da Comissão Organizadora da International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP), em 2004, 2006, 2008  , 2011 , 2015, 2018 e 2023.

• Menção honrosa no Concurso de Prémios Cienttíficos da Universidade Técnica de Lisboa / Santander Totta, em 2011, na área da Matemática.

• Bolsa de Investigação na Universidade de Chester (Reino Unido) em 2013-2014.

• Investigador do Institute of Stochastics da Johannes Kepler University of Linz, Austria, no âmbito do projecto 629496 das Marie Curie Actions – Intra European Fellowships, desde Setembro de 2014, por um ano.

• Investigador esponsável do Projecto POCI-01-0145-FEDER-31393,

   'Análise e simulação numérica de equações de campo neuronal determinísticas e estocásticas com aplicações à robótica ' (NEUROFIELD) ,2018-2021 (36 meses)  . Financiamento: 248000 E  (50% para IST-ID e 50% para UMinho).