Research Summary

Interests

Volterra integral equations and functional-differential equations (differential equations with advances and delays)
Numerical methods for the Neural Field Equations
Numerical approximation of ordinary differential equations

Development Projects

ACES - Applied Computing in Science and Engineering

Development of Master Programs in the fields of Numerical Analysis, Statistics and Computation

Find here some information about this project.

Coordination/Participation in Research Projects

Analysis and numerical simulation of deterministic and stochastic neural field equations with applications to robotics

NEUROFIELD

Funded by FCT, POCI-01-0145-FEDER-031393, 2018-2021
Neural Fields: Stochastic approach and numerical simulations

Marie Curie Fellowship, Funded by EU,2014-2015

NEUROSTOCHSIM
Analytical and Computational Methods for Singular Integral Equations

Funded by FCT, under grant PTDC/MAT/101867/2008 , 2010-2013
Joint Project: IST -University of Chester

Funded by British Council (UK-Portugal), 2008-2009

Accões Integradas Luso-Britânicas
Computational Methods for Singular Problems

POCTI/MAT/45700/2002

Funded by FCT (Portugal), 2003-2006

Cooperation with foreign universities and research centers

Minsk, Belarus

Belarussian National Technical University

Belarussian National Technical University
Moscow, Russia

Computing Centre, Russian Academy o Sciences

Dorodnicyn Computing Centre
Constantine, Algeria

Ecole Normale Superieure de Constantine

Ecole Normale Superieure de Constantine
Tartu, Estonia

Institute of Mathematics and Statistics

Institute of Mathematics and Statistics, University of Tartu, Estonia
Irkutsk, Russia

Institute for System Dynamics and Control Theory

Institute for System Dynamics and Control Theory
São Carlos, Brasil

Instituto de Ciências Matemáticas de São Carlos

Instituto de Ciências Matemáticas de São Carlos
Ribeirão Preto, Brasil

Faculdade de Ciências de Ribeirão Preto

Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto
Vienna - Austria

Institute of Analysis and Scientific Computing

Institute of Analysis and Scientific Computing, ViennaUniversity of Technology
Linz, Austria

Institute of Stochastics, Johannes Kepler Univeristy

Institute of Stochastics, Johannes Kepler Univeristy
Moscow, Russia

Keldysh Institute of Applied Mathematics

Keldysh Institute of Applied Mathematics
Moscow, Russia

Moscow Technological University Stankin

Moscow Technological University Stankin
Moscow, Russia

Moscow State University Lomonossov

Moscow State University Lomonossov
Moscow, Russia

Plekhanov Russian University of Economics

Plekhanov Russian University of Economics
Notingham, UK

School of Mathematical Sciences, University of Notingham, UK

School of Mathematical Sciences, University of Notingham, UK
Chester, UK

University of Chester, UK

University of Chester, UK
Babolsar, Iran

University of Mazandaran, Iran

University of Mazandaran
Maraghe, Iran

University of Maraghe

University of Maraghe, Iran

Current PhD and MSc Students

2023
PhD

Constantino Caetano, Instituto Superior Técnico, Thesis subject: fractional differential equations in Mathematical Epidemiology (Supervised by L. Morgado, Niel Hens and P.Lima)
2023
PhD

Marcos Latas , Faculdade de Medicina da Universidade de Lisboa, Thesis subject: Application of geometric models to the study of intracranian vasculature ( supervised by Catarina Fonseca, Hugo Ferreira and P. Lima)

My Former Students

2022
MSc

Alexandre Cabral, Master Program in Mathematics and Applications, Análise Comparativa de Métodos Numéricos para a Equação do Campo Neuronal, approved in 2022.
2021
MSc

Tiago Sequeira, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical simulations of the two-dimensional stochastic neural field equation, approved in 2021.
2019
MSc

Mariana Mendes, Master Program in Mathematics and Applications, IST. Thesis title: Numerical solution of equations with non-integer order derivative, approved in 2019. (Supervised by Luisa Morgado and P. Lima)
2019
MSc

Madalena França Martins, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical Solution of the One-dimensional Stocastic Neural Field Equation with Delay, approved in 2019
2018
MSc

Paula Guerreiro, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical solution of the two-dimensional neural field equation, approved in 2018
2012
PhD

Filomena Teodoro, Instituto Superior Técnico, Thesis title: Computational Methods for Functional Differential Equations with Deviating Arguments, approved in 2012
2010
PhD

Magda Rebelo, Instituto Superior Técnico, Thesis title: Analytical and Numerical Methods for Nonlinear Integral Equations with Weakly Singular Kernel, approved in 2010 (Supervised by Teresa Diogo and P. Lima)
2008
PhD

Luisa Morgado , Universidade de Trás os Montes e Alto Douro, Thesis title: Analysis and Numerical Approximation of Singular Boundary Value Problems, approved in 2008
2003
PhD

António Oliveira, Universidade Nova de Lisboa, Thesis title: Aproximação numérica e assintótica de problemas de valores de fronteira para equações de Emden-Fowler, approved in 2003
2003
MSc

Matilde Pato, Master Program in Mathematics and Applications, IST. Análise Numérica de problemas de valores de fronteira singulares, approved in 2003
1996
MSc

Isabel Santos, Master Program in Mathematics and Applications, IST. Thesis title:Métodos numéricos para equações integrais de Volterra com núcleo singular, approved in 1996. (Supervised by Teresa Diogo and P.Lima)
1996
PhD

Mário Graça, Instituto Superior Técnico, Thesis title: The IRA Procedures and other Methods in Convergence Acceleration, approved in 1996 (Supervised by Claude Brezinski and P.Lima)
1995
MSc

Cristina Lemos, Master Program in Mathematics and Applications, IST. Thesis title: Resolução de equações de Emden-Fowler pelo método dos elementos finitos, approved in 1995

My Co-Authors

Daniele Avitabile, Vrije Universiteit, Amsterdam
Esmail Babolian, Kharazmy University, Tehran, Iran
Christopher Baker, University of Manchester, UK
Sohrab Bazm, Marageh University, Iran
Evelyn Buckwar , Johannes Kepler University of Linz, Austria
Azzeddine Bellours, Ecole Normale Superieure de Constantine, Algeria
Mikhail Bulatov, Institute of System Dynamics and Control Theory, Irkutsk, Russia
Michel Carpentier , Instituto Superior Técnico , Lisboa,Portugal
Nikolai Chemetov, Universidade de São Paulo, Brasil
Stephen Coombes, University of Nottingham, UK
Teresa Diogo, Instituto Superior Técnico, University of Lisbon, Portugal
Alla Dyshko, Computing Centre, Russian Academy of Sciences
Wolfram Erlhagen, Departamento de Matemática, Universidade do Minho, Portugal
Luisa Fermo, University of Cagliari, Italy
Neide Franco, Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, Brasil
Neville Ford, University of Chester, UK
Judith Ford, University of Chester, UK
Mário Graça, Instituto Superior Técnico, Lisboa, Portugal
G. Hastermann, Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria
Zdislaw Jackiewicz, Arizona State, University , USA
Georg Kitzhofer, Institute for Analysis and Scientific Computing, University of Technology,Vienna, Austria
Othmar Koch, Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria
Marek Kolk, Institute of Applied Mathematics, University of Tartu, Estonia
Nadezda Konyukhova, Computing Center, Russian Academy of Sciences,Moscow, Russia
Gennady Kulikov, CEMAT, Instituto Superior Técnico, Lisboa, Portuga
Maria Kulikova, CEMAT, Instituto Superior Técnico, Lisboa, Portugal
Patricia Lumb, Dept. Mathematics, University of Chester, UK
Athena Makroglou , University of Portsmouth, UK
Luisa Morgado, CEMAT/Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal
Somayeh Nemati, University of Mazandaran, Babolsar, Iran
Donatella Occorsio, University of Basilicata, Italy
António Oliveira, Universidade Nova de Lisboa, Portugal
Yadollah Ordokhani, Alzahra University, Tehran, Iran
Matilde Pato, Instituto Superior de Engenharia, Lisboa, Portugal
Arvet Pedas, Institute of Applied Mathematics, Tartu University,Estonia
Ana Pedro,Universidade Nova de Lisboa, Portugal
Magda Rebelo, Universidade Nova de Lisboa, Portugal
Markus Schoebinger, Institute of Analysis and Scientific Computing, Vienna Austria
Salameh Sedaghat , Buein Zahra Technical University, Iran
Adélia Sequeira, Instituto Superior Técnico, Portugal
Tiago Sequeira, Instituto Superior Técnico, Lisboa
Mikhail Soloviev, Computing Center, Russian Academy of Sciences, Moscow, Russia
Aleksander Sukov,Russian New University, Moscow, Russia
Tao Tang, Hong Kong Baptist University, China
Filomena Teodoro , Escola Naval /CEMAT, Lisboa, Portugal
Sophy Thomas. University of Chester, UK
Than Do Tien, Vietnam Military Medical University, Vietnam
Delfim Torres , Departamento de Matematica, Universidade de Aveiro, Portugal
Konstantin Tregubov , Moscow State Technological University, Moscow, Russia
Gennadi Vainikko, Institute of Applied Mathematics. Tartu University, Estonia
Svilen Valtchev, Instituto Politécnico de Leiria, Portugal
Ewa Weinmüller, Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria

Pedro Lima

Full Professor

Mathematics Department of Instituto Superior Tecnico

Research Summary

Interests

Development Projects

ACES - Applied Computing in Science and Engineering

Development of Master Programs in the fields of Numerical Analysis, Statistics and Computation

Coordination/Participation in Research Projects

Analysis and numerical simulation of deterministic and stochastic neural field equations with applications to robotics

Neural Fields: Stochastic approach and numerical simulations

Analytical and Computational Methods for Singular Integral Equations

Joint Project: IST -University of Chester

Computational Methods for Singular Problems

Cooperation with foreign universities and research centers

Current PhD and MSc Students

Constantino Caetano, Instituto Superior Técnico, Thesis subject: fractional differential equations in Mathematical Epidemiology (Supervised by L. Morgado, Niel Hens and P.Lima)

Marcos Latas , Faculdade de Medicina da Universidade de Lisboa, Thesis subject: Application of geometric models to the study of intracranian vasculature ( supervised by Catarina Fonseca, Hugo Ferreira and P. Lima)

My Former Students

Alexandre Cabral, Master Program in Mathematics and Applications, Análise Comparativa de Métodos Numéricos para a Equação do Campo Neuronal, approved in 2022.

Tiago Sequeira, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical simulations of the two-dimensional stochastic neural field equation, approved in 2021.

Mariana Mendes, Master Program in Mathematics and Applications, IST. Thesis title: Numerical solution of equations with non-integer order derivative, approved in 2019. (Supervised by Luisa Morgado and P. Lima)

Madalena França Martins, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical Solution of the One-dimensional Stocastic Neural Field Equation with Delay, approved in 2019

Paula Guerreiro, Master Program in Mathematics and Applications, IST. Thesis Title: Numerical solution of the two-dimensional neural field equation, approved in 2018

Filomena Teodoro, Instituto Superior Técnico, Thesis title: Computational Methods for Functional Differential Equations with Deviating Arguments, approved in 2012

Magda Rebelo, Instituto Superior Técnico, Thesis title: Analytical and Numerical Methods for Nonlinear Integral Equations with Weakly Singular Kernel, approved in 2010 (Supervised by Teresa Diogo and P. Lima)

Luisa Morgado , Universidade de Trás os Montes e Alto Douro, Thesis title: Analysis and Numerical Approximation of Singular Boundary Value Problems, approved in 2008

António Oliveira, Universidade Nova de Lisboa, Thesis title: Aproximação numérica e assintótica de problemas de valores de fronteira para equações de Emden-Fowler, approved in 2003

Matilde Pato, Master Program in Mathematics and Applications, IST. Análise Numérica de problemas de valores de fronteira singulares, approved in 2003

Isabel Santos, Master Program in Mathematics and Applications, IST. Thesis title:Métodos numéricos para equações integrais de Volterra com núcleo singular, approved in 1996. (Supervised by Teresa Diogo and P.Lima)

Mário Graça, Instituto Superior Técnico, Thesis title: The IRA Procedures and other Methods in Convergence Acceleration, approved in 1996 (Supervised by Claude Brezinski and P.Lima)

Cristina Lemos, Master Program in Mathematics and Applications, IST. Thesis title: Resolução de equações de Emden-Fowler pelo método dos elementos finitos, approved in 1995

My Co-Authors