RESEARCH PAPERS

 

·          Magda Rebelo, Teresa Diogo, Sean McKee, A Mathematical Treatment of the Fluorescent Capillary-Fill Device, to appear in SIAM J. Applied Mathematics

 

·          Teresa Diogo, Gennadi Vainikko, Applicability of spline collocation to cordial Volterra equations,  Mathematical Modelling and Analysis

 

·          Teresa Diogo, Jingtang Ma,  Magda Rebelo,  Analytical and numerical studies of delay Volterra-integro differential equations with noncompact kernels (in preparation)

·         Teresa Diogo, Jingtang Ma, Magda Rebelo,  Fully discretized collocation methods for nonlinear singular Volterra integral equations, (submitted)

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·          T.Diogo, M.Kolk, P.Lima, A.Pedas, High order methods for weakly singular Volterra integro-differential equations,  in: Integral Methods in Science and Engineering,  C.Constanda,  M.E.Perez, Eds., Vol. 2, p. 151-160, Birkhauser, 2010.

·         T. Diogo, P. Lima, M. Rebelo, Extrapolation Methods for a Nonlinear Weakly Singular Volterra Integral Equation,
AIP Conference Proceedings- ICNAAM 2010, Vol. 1281, pp. 1175-1178.        

·          Magda Rebelo and Teresa Diogo,  A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel, J. Comput. Appl. Math.  234 (2010), 2859-2869.

  •   Teresa Diogo, Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations,   J. Comput. Appl. Math. 229 (2009) 363–372.
  • Teresa Diogo,  Pedro Lima, Superconvergence of collocation methods for a class of weakly singular Volterra integral equations,  J. Comput. Appl. Math , 218 (2008), 307-316.
  • Teresa Diogo, Pedro Lima, Collocation solutions of a weakly singular Volterra integral equation, TEMA Tendências da Matemática Aplicada e Computacional,  Vol. 8 (2007), 229-238 .
  • T.Diogo, N.J.Ford, P. Lima, S. Thomas, Solution of a singular integral equation by a split- interval method,   Intern. J.  Num. Anal.  Mod., 4 (2007) 63 -73. 
  • Neville J. Ford, Teresa Diogo, Judith M. Ford, Pedro Lima, Numerical modelling of qualitative behaviour of solutions to convolution integral  equations, J. Comput. Appl. Math. 205 (2007) 849 – 858
  • M.Teresa Diogo, Magda S. Rebelo, Pedro M. Lima, Comparative study of numerical methods for a nonlinear weakly singular Volterra integral equation, HERMIS Journal, Hellenic European Research on Mathematics and Informatics, Vol. 7, 2006.            http://www.aueb.gr/pympe/hermis/hermis-volume-7/
  • T. Diogo, M. Rebelo, P. Lima,  Numerical solution of a nonlinear Abel type Volterra integral equation, Commun. Pure Appl. Anal., 5 (2006) 277-288. 

                                                                                                                      

  • T.Diogo, M.S. Rebelo, P.M. Lima, Computational methods for a nonlinear Volterra integral equation,  Proceedings of the 7th Hellenic European Conference on Computer Mathematics and its Applications (HERCMA 2005), Athens (September 22-24 2005); HERCMA Conference Series, LEA Publishers, ISBN: 960-87275-8-8, 100--107.  
  • T. Diogo, J. T. Edwards, N. J. Ford, S. M. Thomas, Numerical analysis of a singular equation,  Appl. Math. Comput., 167 (2005) 372-382.
  • T.Diogo, N.B. Franco, P. Lima,   High order product integration methods for a Volterra integral equation with logarithmic singular kernel , Commun. Pure Appl. Anal., 3 (2004) 217--235. 
  • T.Diogo, S.Valtchev, Numerical solution of a singular Volterra integral equation by piecewise polynomial collocation, (Proc. of Ninth International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science(EPMESC IX), 25-28 November 2003, Macau ), in:  Computational Methods in Engineering and Science,  Iu ,Lamas, Li and Mok. (Eds.),  Swets & Zellinger, Lisse, 2003, 195--200.  (ISI)
  • T.Diogo, P.Lima, S.Valtchev, N. Ford, Numerical methods for a nonuniquely solvable Volterra integral equation, in: Proc. of the Iberian-Latin-American Congress on Computational Methods in Engineering (XXIV CILAMCE), Ouro Preto, Brazil, 2003. IN CD-ROM .
  • T.Diogo, S. Valtchev, Collocation methods for a Volterra integral  equation with multiple solutions, in: Fundamental Physical-Mathematical Problems and Modelling of Technological Systems, N.6, Janus-K Editor, Moscow, 2003.

 

  • T.Diogo, P.Lima, A comparative study of numerical methods for a certain Volterra integral equation with weakly singular kernel, in: 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.), vol. 2,  574-582 (2002) 
  • T.Diogo, P.Lima, Numerical solution of a non-uniquely solvable Volterra integral equation, (Proc.of the 3rd International Conference FDS2000, 1-4 Setember 2000, Palanga, Lituania), in: Finite difference schemes: theory and applications, R.Ciegis, A.Samarskii and M.Sapagovas (Eds.), 39--48.
  • T.Diogo, N.B.Franco, P.Lima, Analysis of product integration methods for a class of singular Volterra integral equations (Proc. XXII CNMAC 99, Santos, Brazil), in: TEMA Tendências da Matemática Aplicada e Computacional  1 (2000), Nº2, 373--387.
  • N.B.Franco, T.Diogo, Métodos de diferenças regressivas para solução de uma equação integral de Volterra de segunda espécie, Anais da XIX CNMAC, SBMAC (1996) 349--351.
  • T.Diogo, N.B. Franco, Solução numérica de uma equação integral de Volterra de segunda espécie,  Anais da  XVII CNMAC, SBMAC (1995) vol.II, 594--597.
  •  T.Diogo, S. McKee, T.Tang, A Hermite-type collocation method for the solution of an integral equation with a certain weakly singular kernel,  IMA J. Num. Anal.  11 (1991) 595--605.
  • T.Diogo, G.J. Makinson, The solution of a Volterra integral equation using B-splines, Mathematical Institute,  University of Kent at Canterbury, UK, 1989 (unpublished).
  • A.C.Freitas, T.Diogo, M.Minhoto, Polynomial splines in one variable as solutions of differential equations, Trabalhos de Investigação, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 1985.

Thesis

  • Collocation-type Methods for Volterra Integral Equations,  Ph.D. Thesis, University of Kent at Canterbury, UK (1991)

Supervisors: Dr. G. Makinson,  University of Kent at Canterbury   and  Prof. Sean McKee, University of Strathclyde, Glasgow, UK