Numerical Methods 
for ODE's and Integral Equations

Articles on the subject

• M. Carpentier and P.M. Lima. Approximation of a class of differential equations using a generalization of the Frobenius method. Preprint DM 27/2000. Submitted for publication.
• T. Diogo and P.M. Lima. Numerical solution of a non-uniquely solvable Volterra integral equation using extrapolation methods. J. Comp. Appl. Math., 140:537--557, 2002.
• A.L. Dyshko, M.P. Carpentier, N.B. Konyukhova, and P.M. Lima. Singular problems for Emden-Fowler type second-order non-linear ordinary differential equations. Journal of Computational Mathematics and Mathematical Physics, 41(4):557--580, 2001. In Russian.
• T. Diogo and P.M. Lima. Numerical solution of a non-uniquely solvable Volterra integral equation. In R. Ciegis, A. Samarskii, and M. Sapagovas, editors, Finite Difference Schemes: Theory and Applications, pages 39--49. IMI, Vilnius, 2000. Proceedings of the 3rd International Conference FDS2000, Palanga, Lituânia.
• T. Diogo, P.M. Lima, and N. Franco. Analysis of product integration methods for a class of singular Volterra integral equations. In Tendências da Matemática Aplicada e Computacional, Vol. 1(2), pages 373--387. Sociedade Brasileira de Matemática Aplicada e Computacional, 2000. Proc. XXII CNMAC 99, Santos.
• P.M. Lima and M. Carpentier. Numerical solution of a singular boundary-value problem in non-Newtonian fluid mechanics. Computer Physics Communications, 126:114--120, 2000.
• P.M. Lima and A. Oliveira. Aproximação de problemas de valores de fronteira singulares usando subsoluções e supersoluções. In Tendências da Matemática Aplicada e Computacional, Vol. 1(2), pages 401--414. Sociedade Brasileira de Matemática Aplicada e Computacional, 2000. Proc. XXII CNMAC 99, Santos.
• P.M. Lima and A. Oliveira. Aproximação numérica de problemas de valores de fronteira com aplicações em mecãnica. In P. Vila Real and J. Grácio, editors, Actas do VI Congresso de Mecânica Aplicada e Computacional, Aveiro, pages 1615--1626. Universidade de Aveiro, 2000.
• P.M. Lima and A. Oliveira. Numerical solution of nonlinear singular boundary-value problems using variable substitutions. In R. Ciegis, A. Samarskii, and M. Sapagovas, editors, Finite Difference Schemes: Theory and Applications, pages 153--162. IMI, Vilnius, 2000. Proceedings of the 3rd International Conference FDS2000, Palanga, Lituânia.
• S. McKee, T. Tang, and T. Diogo. An Euler-type method for two-dimensional Volterra integral equations of the first kind. IMA Journal of Numerical Analysis, 3:423--440, 2000.
• M.P. Carpentier and P.M. Lima. Numerical solution of a sublinear singular boundary-value problem. In J. Bento, E.A. Oliveira, and E. Pereira, editors, EPMESC VII -- International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science, pages 119--129. Elsevier, 1999.
• P.M. Lima and M. Carpentier. Asymptotic expansions and numerical approximation of non-linear degenerate boundary-value problems. Applied Numerical Mathematics, 30(1):93--111, 1999.
• P.M. Lima and M. Carpentier. Iterative methods for a singular boundary-value problem. Journal of Computational and Applied Mathematics, 111(1):173--186, 1999.
• P.M. Lima and T. Diogo. An extrapolation method for a Volterra integral equation with weakly singular kernel. Applied Numerical Mathematics, 24:131--148, 1997.
• P.M. Lima. Numerical methods and asymptotic error expansions for the Emden-Fowler equations. Journal of Computational and Applied Mathematics, 70:245--266, 1996.



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