Bibliography for Picard Iteration

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  1. Approximating fixed points of weak phi-contractions using the Picard iteration.  
    Berinde, Vasile
    Fixed Point Theory  4  (2003),  no. 2, 131--142, MathSciNet.  
  2. Picard Iteration for Nonsmooth Equations
    Sheng, Song-bai; Xu, Hui-fu
    Journal of Computational Mathematics, November, 2001, vol. 19, no. 6, pp. 583-590, MathSciNet.  
  3. Picard iterations for solution of nonlinear equations in certain Banach spaces.
    Moore, Chika
    J. Math. Anal. Appl. 245 (2000), no. 2, 317--325, MathSciNet.  
  4. C11 convergence of Picard's successive approximations  
    Izzo, Alexander J.
    Proceedings of the american mathematical society, 1999, vol. 127, no. 7, pp. 2059, Ingenta.  
  5. On a Theorem of Picard  
    F. Gesztesy; W. Sticka  
    Proceedings of the American Mathematical Society, Vol. 126, No. 4. (Apr., 1998), pp. 1089-1099, Jstor.  
  6. An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions  
    K. Lust, D. Roose
    SIAM Journal on Scientific Computing, Volume 19, Number 4, (1998), pp. 1188-1209.  
  7. Picard Iteration Method, Chebyshev Polynomial Approximation, and Global Numerical Integration of Dynamical Motions.
    Fukushima, Toshio
    The Astronomical journal, 1997, vol. 113, no. 5, pp. 1909, Ingenta.  
  8. Implementing the Picard iteration.
    Parker, G. Edgar; Sochacki, James S.
    Neural Parallel Sci. Comput. 4 (1996), no. 1, 97--112, MathSciNet.  
  9. The Picard Iterative approximation to the solution of the integral equation of radiative transfer - Part I. The plane-parallel case.
    Kuo, Kwo-Sen; Weger, Ronald C.; Welch, Ronald M.
    Journal of Quantitative Spectroscopy and Radiative Transfer, v 53, n 4, Apr, 1995, p 425, Ingenta.  
  10. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems.
    Paniconi, Claudio; Putti, Mario
    Water resources research, 1994, vol. 30, no. 12, pp. 3357, Ingenta.  
  11. Picard iteration convergence analysis in a Galerkin finite element approximation of the one-dimensional shallow water equations.
    Cathers, B.; O'Connor, B. A.
    Numerical Methods for Partial Differential Equations, v 9, n 1, Jan, 1993, p 77-92, MathSciNet.  
  12. Chebyshev acceleration of Picard-Lindelof iteration.
    Lubich, Ch.
    BIT, 1992, no. 3, pp. 535, Ingenta.  
  13. Linear Acceleration of Picard-Lindelof Iteration.
    Nevanlinna, O.
    Numerische mathematik, 1990, vol. 57, no. 2, pp. 147, Ingenta.  
  14. Symbolic Computational Algebra Applied to Picard Iteration
    Mathews, John
    Mathematics and Computer Education Journal, 1989, Vol. 23, No. 2, pp. 117, Ingenta.  
  15. Comparison of Picard and Newton iterative methods for unconfined groundwater flows
    Mohan Kumar, M.S.; Sridharan, K.; Lakshmana Rao, N.S.
    Journal of the Institution of Engineers (India), Part CI: Civil Engineering Division, v 68 pt 6, May, 1988, p 266-271, Compendex.  
  16. Application of picard-chebyshev iteration and an extended procedure to an elastica problem
    Chakrabarti, S.; Rao, C.V. Joga
    Congress of the Indian Society of Theoretical and Applied Mechanics, 1985, p 207, Compendex.  
  17. Picard Iterations Of Boundary-Layer Equations.
    Ardema, M. D.; Yang, L.
    AIAA Paper, 1985, p 669-678, Compendex.  
  18. Some experiments with Picard's iteration for second-order nonlinear boundary value problems.
    Meek, D. S.; Usmani, R. A.
    Proceedings of the fourteenth Manitoba conference on numerical mathematics and computing (Winnipeg, Man., 1984). Congr. Numer. 46 (1985), 201--210, MathSciNet.  
  19. A comparison of the iterative method and Picard's successive approximations for deterministic and stochastic differential equations.
    Adomian, G.; Malakian, K.
    Appl. Math. Comput. 8 (1981), no. 3, 187--204, MathSciNet.  
  20. A Relaxed Picard Iteration Process for Set-Valued Operators of the Monotone Type  
    J. C. Dunn  
    Proceedings of the American Mathematical Society, Vol. 73, No. 3. (Mar., 1979), pp. 319-327, Jstor.  
  21. Solutions Of The Diffusion Equation By Picard's Iteration Procedure.
    Moalem-Maron, D.; Meinhardt, Y. Roberto
    Letters in Heat and Mass Transfer, v 5, n 5, Sep-Oct, 1978, p 269-277, Compendex.  
  22. Self-Regulating Picard-Type Iteration For Computing The Periodic Response Of A Nearly Linear Circuit To A Periodic Input.
    Neill, T. B. M.; Stefani, Jane
    Electronics Letters, v 11, n 17, Aug 21, 1975, p 413-415, Compendex.  
  23. Picard's Theorem (in Classroom Notes)  
    James Fabrey  
    The American Mathematical Monthly, Vol. 79, No. 9. (Nov., 1972), pp. 1020-1023, Jstor.  
  24. On the region of convergence of Picard's iteration.
    van de Craats, J.
    Z. Angew. Math. Mech. 52 (1972), no. 9, 487--491, MathSciNet.  
  25. On Iteration Procedures for Equations of the First Kind, Ax = y, and Picard's Criterion for the Existence of a Solution  
    J. B. Diaz; F. T. Metcalf  
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 923-935, Jstor.  
  26. Convergence of Picard's Method for |lambda| > |lambda1| (in Mathematical Notes)  
    J. W. Burgmeier; M. R. Scott  
    The American Mathematical Monthly, Vol. 77, No. 8. (Oct., 1970), pp. 865-867, Jstor.  
  27. On the interval of convergence of Picard's iteration.
    Bailey, P. B.
    Z. Angew. Math. Mech. 48 1968 127--128, MathSciNet.  
  28. On the Cauchy-Picard Method  
    Arthur Wouk  
    The American Mathematical Monthly, Vol. 70, No. 2. (Feb., 1963), pp. 158-162, Jstor.  
  29. Note on the Picard Method of Successive Approximations  
    Dunham Jackson  
    The Annals of Mathematics, 2nd Ser., Vol. 23, No. 1. (Sep., 1921), pp. 75-77, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004