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PUBLICATIONS OF Z. JACKIEWICZ

  1. On the convergence of multistep methods for the Cauchy problem for ordinary differential equations (with M. Kwapisz), Computing 20 (1978), 351-361.
  2. Convergence of multistep methods for Volterra functional differential equations, Numer. Math. 32 (1979), 307-332.
  3. On numerical integration of implicit ordinary differential equations (with M. Kwapisz), Apl. Mat. 26 (1981), 97-110.
  4. One step methods for the numerical solution of Volterra functional differential equations of neutral type, Applicable Anal. 12 (1981), 1-11.
  5. The numerical solution of Volterra functional differential equations of neutral type, SIAM J. Numer. Anal. 18 (1981), 615-626.
  6. Adams methods for neutral functional differential equations, Numer. Math. 39 (1982), 221-230.
  7. The numerical solution of Volterra integro-functional equations (with M. Kwapisz), In: Functional-Differential Systems and Related Topics II, Proceedings of the Second International Conference (M. Kisielewicz, ed.), Blazejewko, Poland, May 3-10, 1981, pp. 141-146, Technical University of Zielona Gora, Zielona Gora 1982.
  8. Some remarks on convergence of multistep methods for approximate solution of functional differential equations (with M. Kwapisz). In: Differential Equations and Applications, Proceedings of the Second Conference, Rousse, Bulgaria, June 29-July 4, 1981, pp. 865-883, Technical University-Rousse, Center of Mathematics, Rousse 1982.
  9. Predictor-corrector methods for the numerical solution of neutral functional-differential equations. In: Proceedings of the Conference ``Numerical Analysis of Parametrized Nonlinear Equations'' (J. F. Porter, ed.), March 24-26, 1983, pp. 14-23, University of Arkansas, Fayetteville 1983.
  10. Global error estimation in the numerical solution of retarded differential equations by Euler's method, Apl. Mat. 28 (1983), 177-185.
  11. Convergence of multistep methods for Volterra integro-differential equations (with M. Kwapisz), Ann. Polon. Math. 43 (1983), 177-185.
  12. Asymptotic stability analysis of theta-methods for functional differential equations, Numer. Math. 43 (1984), 389-396.
  13. One step methods of any order for neutral functional differential equations, SIAM J. Numer. Anal. 21 (1984), 186-511.
  14. Stability analysis of numerical methods for Volterra integral equations of the second kind (with V. Bakke). In: Proceedings of the Conference ``Estimation and Control of Distributed Systems'' (Z. Jackiewicz, ed.), Fayetteville, Arkansas, April 12-14, 1984, pp. 1-17, University of Arkansas, Fayetteville 1984.
  15. Global error estimation in the numerical solution of integro-differential equations by Euler's method, Zastos. Mat. 18 (1984), 487-501.
  16. A note on the stability of theta-methods for Volterra integral equations of the second kind (with M. Kwapisz), Czechoslovak Math. J. 34 (1984), 349-354.
  17. Stability analysis of reducible quadrature methods for Volterra integral equations of the second kind (with V. Bakke), Numer. Math. 47 (1985), 159-173.
  18. Stability analysis of reducible quadrature methods for Volterra integral equations of the first kind (with V. Bakke), J. Integral Equations 9 (1985), 243-249.
  19. Quasilinear multistep methods and variable step predictor-corrector methods for neutral functional differential equations, SIAM J. Numer. Anal. 23 (1986), 423-452.
  20. Stability analysis of linear multistep methods for delay differential equations (with V. Bakke), Internat. J. Math. Math. Sci. 9 (1986), 447-458.
  21. Stability analysis of product theta-methods for Abel integral equations of the second kind (with V. Bakke), Numer. Math. 48 (1986), 127-136.
  22. Boundedness of solutions of difference equations and application to numerical solution of Volterra integral equations of the second kind (with V. Bakke), J. Math. Anal., Appl. 115 (1986), 592-605.
  23. The numerical integration of Volterra integro-differential equations (with V. Bakke), Rev. Roumaine Math. Pures Appl. 31 (1986), 275-282.
  24. Existence and uniqueness of solutions of neutral delay differential equations with state dependent delays, Funkcial. Ekvac. 30 (1987), 9-17.
  25. Stability analysis of reducible quadrature methods for Volterra integro-differential equations (with V. Bakke), Apl. Mat. 32 (1987), 37-48.
  26. Stability analysis of modified multilag methods for Volterra integral equations, IMA J. Numer. Anal. 7 (1987), 473-484.
  27. The numerical solution of Volterra integro-functional equations (with M. Kwapisz), Zastos. Mat. 19 (1987), 341-357.
  28. Variable step variable order algorithm for the numerical solution of functional-differential equations, Appl. Numer. Math. 3 (1987), 317-329.
  29. Stability of numerical methods for Volterra integro-differential equations of convolution type (with V. Bakke), Z. Angew. Math. Mech. 68 (1988), 89-100.
  30. Stability analysis of one-step methods for neutral delay-differential equations (with A. Bellen and M. Zennaro), Numer. Math. 52 (1988), 605-619.
  31. Fully implicit one-step methods for neutral functional-differential equations, Proc. of 27th IEEE Conf. of Dec. and Control (1988), pp. 813-816 (Invited paper).
  32. Stability analysis of Volterra integro-differential equation (with M. Klaus and C. O'Cinneide), J. Integral Equations Appl. 1 (1988), 501-516.
  33. Natural continuous extensions of Runge-Kutta methods for Volterra integral equations of the second kind and their applications (with A. Bellen, R. Vermiglio and M. Zennaro), Math. Comp. 52 (1989), 49-63.
  34. The numerical solution of boundary-value problems for differential equations with state depending deviating arguments (with V. Bakke), Apl. Mat. 34 (1989), 1-17.
  35. Global stability condition for collocation methods for Volterra integral equations of the second kind (with M. R. Crisci, E. Russo and A. Vecchio), J. Integral Equations Appl. 2 (1989), 49-58.
  36. One-step methods for neutral delay-differential equations with state dependent delays, Zastos. Mat. 20 (1990), 445-463.
  37. Stability analysis of Runge-Kutta methods for Volterra integral equations of the second kind (with A. Bellen, M. Zennaro and R. Vermiglio), IMA J. Numer. Anal. 10 (1990), 103-118.
  38. Unstable neutral functional-differential equations (with A. Feldstein), Canad. Math. Bull. 33 (1990), 428-433.
  39. Global stability analysis of the Runge-Kutta methods for Volterra integral and integro-differential equations with degenerate kernels (with M.R. Crisci, E. Russo and A. Vecchio), Computing 45 (1990), 291-300.
  40. Stability analysis of trapezoidal method for Volterra integral equations with completely positive kernels (with A. Bellen, R. Vermiglio and M. Zennaro), J. Math. Anal. Appl. 152 (1990), 324-342.
  41. Stability analysis of time-point relaxation Heun method (with A. Bellen and M. Zennaro), Report ``Progretto Finalizatto Sistemi Informatici e Calcolo Parallelo,'' 1/30, 1990.
  42. The numerical solution of neutral functional-differential equations by Adams predictor-corrector methods (with E. Lo), Appl. Numer. Math. 8 (1991), 477-491.
  43. Two-step Runge-Kutta methods (with R. Renaut and A. Feldstein), SIAM J. Numer. Anal. 28 (1991), 1165-1182.
  44. Stability analysis of discrete recurrence equations of Volterra type with degenerate kernels (with M.R. Crisci, E. Russo and A. Vecchio), J. Math. Anal. Appl. 162 (1991), 49-62.
  45. Stability analysis of exact collocation methods for Volterra integro-differential equations (with M. R. Crisci, E. Russo and A. Vecchio), Atti Sem. Mat. Fis. Univ. Modena. 39 (1991), 527-536.
  46. The numerical solution of functional differential equations: A survey (with M. Kwapisz), Mat. Stos. 33 (1991), 57-78.
  47. Two-step error estimators for singly-implicit Runge-Kutta methods (with A. Bellen and M. Zennaro), In: Proc. of the 13th IMACS World Congress on Comput. and Appl. Math. (R. Vichnevetsky and J.J. H. Miller, eds), p. 297, Criterion Press, Dublin 1991.
  48. Stability analysis of waveform-relaxation Runge-Kutta methods (with A. Bellen and M. Zennaro), In: Proc. of the 13th IMACS World Congress on Comput. and Appl. Math. (R. Vichnevetsky and J.J.H. Miller, eds), pp. 271-272, Criterion Press, Dublin 1991.
  49. Stability analysis of multilag and modified multilag methods for Volterra integro-differential equations (with V. Bakke), IMA J. Numer. Anal. 12 (1992), 243-257.
  50. Local error estimation for singly-implicit formulas by two-step Runge-Kutta methods (with A. Bellen and M. Zennaro), BIT 32 (1992), 104-117.
  51. Variable stepsize explicit two-step Runge-Kutta methods (with M. Zennaro), Math. Comp. 59 (1992), 421-438.
  52. Time-point relaxation Runge-Kutta methods for ordinary differential equations (with A. Bellen and M. Zennaro), J. Comput. Appl. Math. 45 (1993), 121-137.
  53. Stability analysis of time-point relaxation Runge-Kutta methods with respect to tridiagonal systems of differential equations, Appl. Numer. Math. 11 (1993), 189-209.
  54. The algorithm SNDDELM for the numerical solution of systems of neutral delay diffferential equations (with E. Lo), Appendix in: Delay Differential Equations with Applications in Population Dynamics by Y. Kuang, Academic Press, Boston 1993.
  55. Diagonally implicit general linear methods for ordinary differential equations (with J.C. Butcher), BIT 33 (1993), 452-472.
  56. Contractivity of waveform relaxation Runge-Kutta methods for dissipative systems in the maximum norm (with A. Bellen and M. Zennaro), SIAM J. Numer. Anal. 31 (1994), 499-523.
  57. A representation formula for two-step Runge-Kutta methods (with S. Tracogna),In: Proc. of the Second Hellenic European Conference on Mathematics and Informatics (E.A. Lipitakis, ed.), September 22-24, pp. 111-120, Hellenic Mathematical Society, Athens, Hellas 1994.
  58. The numerical integration of neutral functional-differential equations by fully implicit one-step methods (with E. Lo), Z. Angew. Math. Mech. 75 (1995), 207-221.
  59. Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations (with R. Vermiglio and M. Zennaro), Appl. Numer. Math. 16 (1995), 343-367.
  60. Numerical simulation of transient stability of power systems by adaptive Runge-Kutta methods (with N. Zhu, A. Bose and D. Tylavsky), Z. Angew. Math. Mech. 75 (1995), 471-480.
  61. A general class of two-step Runge-Kutta methods for ordinary differential equations (with S. Tracogna), SIAM J. Numer. Anal. 32 (1995), 1390-1427.
  62. A note on existence and uniqueness of solutions of neutral differential equations with state dependent delays, Comment. Math. Univ. Carolin. 36 (1995), 15-17.
  63. Explicit two-step Runge-Kutta methods (with R. Renaut and M. Zennaro), Appl. Math. 40 (1995), 433-456.
  64. Convergence of Picard and modified Picard iterations for neutral functional differential equations (with M. Kwapisz), In: Proc. of the First International Conference on Difference Equations (S.N. Elaydi, J.R. Graef, G. Ladas, A.C. Peterson, eds.), May 25-28, 1994, pp. 263-273, Gordon and Breach Publishers, Australia 1995.
  65. The performance of preconditioned waveform relaxation techniques for pseudospectral methods (with K. Burrage and R. Renaut), Numerical Methods for Partial Differential Equations 12 (1996), 245-263.
  66. Preconditioning waveform relaxation iterations for differential systems (with K. Burrage, S.P. Nørsett and R. Renaut), BIT 36 (1996), 54-76.
  67. Acceleration of convergence of waveform relaxation iterations for second order linear systems (with J. Knap), Transactions of the CSME 20 (1996), 87-103.
  68. Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations (with S. Tracogna), Numerical Algorithms 12 (1996), 347-368.
  69. Convergence of waveform relaxation methods for differential-algebraic systems (with M. Kwapisz), SIAM J. Numer. Anal. 33 (1996), 2303-2317.
  70. General linear methods with external stages of different orders (with R. Vermiglio), BIT 36 (1996), 688-712.
  71. Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations (with J.C. Butcher), Appl. Numer. Math. 21 (1996), 385-415.
  72. Regularity properties of Runge-Kutta methods for ordinary differential equations (with R. Vermiglio and M. Zennaro), Appl. Numer. Math. 22 (1996), 251-262.
  73. Waveform relaxation methods for functional differential systems of neutral type (with M. Kwapisz and E. Lo), J. Math. Anal. Appl. 207 (1996), 255-285.
  74. Nonlinear optimization approach to construction of general linear methods of high order (with J.C. Butcher and H.D. Mittelmann), J. Comp. Appl. Math. 81 (1997), 181-196.
  75. Regularity properties of Runge-Kutta methods for delay differential equations (with R. Vermiglio and M. Zennaro), Appl. Numer. Math. 24 (1997), 265-278.
  76. Implementation of diagonally implicit multistage integration methods for ordinary differential equations (with J.C. Butcher), SIAM J. Numer. Anal. 34 (1997), 2119-2141.
  77. Regularity properties of multistage integration methods (with R. Vermiglio and M. Zennaro), J. Comp. Appl. Math. 87 (1997), 285-302.
  78. Nordsieck representation of DIMSIMs (with J.C. Butcher and P. Chartier), Numerical Algorithms 16 (1997), 209-230.
  79. Construction of high order DIMSIMs for ordinary differential equations (with J.C. Butcher), Appl. Numer. Math. 27 (1998), 1-12.
  80. Block Toeplitz preconditioning for static and dynamic linear systems (with K. Burrage and B. Welfert), Linear Algebra Appl. 279 (1998), 51-74.
  81. Construction of two-step Runge-Kutta methods of high order for ordinary differential equations (with Z. Bartoszewski), Numerical Algorithms 18 (1998), 51-70.
  82. Convergence analysis of waveform relaxation methods using pseudospectra (with B. Owren and B. Welfert), Comput. Math. Appl. 36 (1998), 67-85.
  83. Frequency analysis of preconditioned waveform relaxation iterations (with A. Augustynowicz), Appl. Math. (Warsaw) 26 (1999), 229-242.
  84. Exploiting structure in the construction of DIMSIMs (with H.D. Mittelmann), J. Comp. Appl. Math. 107 (1999), 233-239.
  85. Experiments with a variable-order type 1 DIMSIM code (with J.C. Butcher and P. Chartier), Numerical Algorithms 22 (1999), 237-261.
  86. Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation (with R. Renaut), Appl. Numer. Math. 34 (2000), 219-229.
  87. Order conditions for partitioned Runge-Kutta methods (with R. Vermiglio), Appl. Math. 45 (2000), 301-316.
  88. Step-control stability of diagonally implicit multistage integration methods, New Zealand J. of Math. 29 (2000), 193-201.
  89. Construction of Runge-Kutta methods of Crouch-Grossman type of high order (with A. Marthinsen and B. Owren), Adv. in Comp. Math. 13 (2000), 405-415.
  90. Acceleration of convergence of static and dynamic iterations (with K. Burrage, G. Hertono and B. Welfert), BIT 41 (2001), 645-655.
  91. A reliable error estimation for DIMSIMs (with J.C. Butcher), BIT 41 (2001), 656-665.
  92. Toward a two-step Runge-Kutta code for nonstiff differential systems (with Z. Bartoszewski), Appl. Math. (Warsaw) 28 (2001), 353-365.

    Recent Papers of Z. Jackiewicz
    (some papers can be downloaded as pdf files)

  93. Implementation of DIMSIMs for stiff differential systems, Appl. Numer. Math. 42 (2002), 251-267.
  94. A note on stability of pseudospectral methods for wave propagation (with R. Renaut), J. Comp. Appl. Math. 143 (2002), 127-139.
  95. Stability analysis of two-step Runge-Kutta methods for delay differential equations (with Z. Bartoszewski), Comput. Math. Appl. 44 (2002), 83-93.
  96. Absorbing boundary conditions of the second order for the pseudospectral Chebyshev methods for wave propagation (with A. Gelb and B. Welfert), SIAM J. Sci. Comput. 17 (2002), 501-512.
  97. Error Estimation for Nordsieck methods (with J.C. Butcher), Numerical Algorithms 31 (2002), 75-85.
  98. Derivation and implementation of two-step Runge-Kutta pairs (with J.H. Verner), Japan J. Industr. Appl. Math. 19 (2002), 227-248.
  99. Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation (with B.D. Welfert), J. Sci. Comput. 18 (2003), 287-313.
  100. A new approach to error estimation for general linear methods (with J.C. Butcher), Numer. Math. 95 (2003), 487-502.
  101. Construction of two-step Runge-Kutta methods with large regions of absolute stability (with J. Chollom), J. Comp. Appl. Math. 157 (2003), 125-137.
  102. Determination of optimal parameters for the Chebyshev-Gegenbauer reconstruction methods, SIAM J. Sci. Comput. 25 (2003/2004), 1187-1198.
  103. Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods (with B.D. Welfert and B. Zubik-Kowal), J. Sci. Comput. 20 (2004), 1-28.
  104. Construction of highly stable two-step W-methods for ordinary differential equations (with H. Podhaisky and R. Weiner), J. Comp. Appl. Math. 167 (2004), 389-403.
  105. Construction of general linear methods with Runge-Kutta stability properties (with J.C. Butcher), Numerical Algorithms. 36 (2004), 53-72.
  106. Unconditionally stable general linear methods for ordinary differential equations (with J.C. Butcher), BIT 44 (2004), 557-570.
  107. Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations (with Z. Bartoszewski), Appl. Numer. Math. 53 (2005), 149-163.
  108. Spectral collocation and waveform relaxation methods with Gegenbauer reconstruction for nonlinear conservation laws (with B. Zubik-Kowal), Comput. Methods Appl. Math. 5 (2005), 51-71.
  109. Determining analyticity for parameter optimization of the Gegenbauer reconstruction method(with A. Gelb), J. Sci. Comput. 27 (2005), 1014-1031.
  110. Construction and implementation of general linear methods for ordinary differential equations. A review, J. Sci. Comput. 25 (2005), 29-49.
  111. Numerical solution of a problem in the theory of epidemics (with F.C. Hoppensteadt), Appl. Numer. Math. 56 (2006), 533-543.
  112. Numerical solution of a Fredholm integro-differential equation modelling neural networks (with M. Rahman and B.D. Welfert), Appl. Numer. Math. 56 (2006), 423-432.
  113. Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations (with B. Zubik-Kowal), Appl. Numer. Math. 56 (2006), 433-443.
  114. Numerical solution of neutral functional differential equations by Adams methods in divided difference form (with E. Lo), J. Comput. Appl. Math. 189 (2006), 592-605.
  115. Stochastic approximations of perturbed Fredholm Volterra integro-differential equation arising in mathematical neurosciences (with M. Rahman and B.D. Welfert), to appear in Appl. Math. Comput.
  116. Derivation of continuous explicit two-step Runge-Kutta methods of order three (with Z. Bartoszewski), to appear in J. Comput. Appl. Math.
  117. Error propagation of general linear methods for ordinary differential equations (with J.C. Butcher and W.M. Wright), to appear in J. Complexity
  118. Spectral approximation of time windows in the solution of dissipative linear differential equations (with K. Burrage and B. Welfert), submitted

Rev. 1/22/2007


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Jackiewicz
Mon. Nov 1 09:12:42 MST 2004