Prof. Dr. Kai Diethelm

Publications

1. Modified Compound Quadrature Rules for Strongly Singular Integrals.
   Computing 52 (1994), 337-354. [MR 95e:65021; Zbl. Math. 809.41026]
   Abstract and link to full text

2. Non-Optimality of Certain Quadrature Rules for Cauchy Principal Value Integrals.
   Z. Angew. Math. Mech. 74 (1994), T689-T690. [Zbl. Math. 802.65017]
   Abstract

3. Uniform Convergence of Optimal Order Quadrature Rules for Cauchy Principal Value Integrals.
   J. Comput. Appl. Math. 56 (1994), 321-329. [MR 97a:65026; Zbl. Math. 821.41027]
   Abstract and link to full text

4. Error Estimates for a Quadrature Rule for Cauchy Principal Value Integrals.
   Proc. Sympos. Appl. Math. 48 (1994), 287-291. [MR 95j:65017; Zbl. Math. 815.41024]
   Abstract

5. The Order of Convergence of Modified Interpolatory Quadratures for Singular Integrals of Cauchy Type.
   Z. Angew. Math. Mech. 75 (1995), S621-S622.
   Abstract

6. Gaussian Quadrature Formulae of the Third Kind for Cauchy Principal Value Integrals: Basic Properties and Error Estimates.
   J. Comput. Appl. Math. 65 (1995), 97-114. [MR 96m:65024; Zbl. Math. 847.41019]
   Abstract and link to full text

7. Asymptotically Sharp Error Bounds for a Quadrature Rule for Cauchy Principal Value Integrals Based on Piecewise Linear Interpolation.
   Approx. Theory Appl. (N. S.) 11 (1995), No. 4, 78-89. [MR 97h:65027; Zbl. Math. 851.41025]
   DOI 10.1007/BF02836832
   Abstract and link to full text

8. Peano Kernels and Bounds for the Error Constants of Gaussian and Related Quadrature Rules for Cauchy Principal Value Integrals.
   Numer. Math. 73 (1996), 53-63. [MR 97f:65016; Zbl. Math. 857.41027]
   Abstract and link to full text

9. A Definiteness Criterion for Linear Functionals and its Application to Cauchy Principal Value Quadrature.
   J. Comput. Appl. Math. 66 (1996), 167-176. [MR 97c:41033; Zbl. Math. 853.41016]
   Abstract and link to full text

10. Error Bounds for Compound Quadratures for Hadamard-Type Finite-Part Integrals.
    In G. Alefeld, J. Herzberger (Eds.): Numerical Methods and Error Bounds. Akademie-Verlag, Berlin (1996), 58-63. [MR 98e:65013]
    Abstract

11. Definite Quadrature Formulae for Cauchy Principal Value Integrals.
    Bolyai Soc. Math. Stud. 5 (1996), 175-186. [MR 97m:41031; Zbl. Math. 860.41028]
    Abstract

12. An Algorithm for the Numerical Solution of Differential Equations of Fractional Order.
    Elec. Transact. Numer. Anal. 5 (1997), 1-6. [MR 98k:65037; Zbl. Math. 890.65071]
    Abstract and link to full text

13. Generalized Compound Quadrature Formulae for Finite-Part Integrals.
    IMA J. Numer. Anal. 17 (1997), 479-493. [MR 98f:65030; Zbl. Math. 871.41021]
    Abstract

14. Peano Kernels of Non-Integer Order.
    Z. Anal. Anwendungen 16 (1997), 727-738. [MR 98i:41043; Zbl. Math. 880.41022]
    Abstract

15. New Error Bounds for Modified Quadrature Formulas for Cauchy Principal Value Integrals.
    J. Comput. Appl. Math. 82 (1997), 93-104. [MR 98g:41032; Zbl. Math. 880.41024]
    Abstract and link to full text

16. A Fractional Version of the Peano-Sard Theorem.
    Numer. Funct. Anal. Optim. 18 (1997), 745-757. [MR 99b:41025; Zbl. Math. 892.41018]
    Abstract and link to full text

17. (with G. Walz) Numerical Solution of Fractional Order Differential Equations by Extrapolation.
    Numer. Algorithms 16 (1997), 231-253. [MR 99e:26006; Zbl. Math. 926.65070]
    Abstract and link to full text

18. Error Bounds for Spline-Based Quadrature Methods for Strongly Singular Integrals.
    J. Comput. Appl. Math. 89 (1998), 257-261. [MR 99e:65037; Zbl. Math. 908.41022]
    Erratum: J. Comput. Appl. Math. 142 (2002), 449-450. [MR 2003f:65038]
    Abstract and links to full text and erratum

19. Fractional Error Constants for Quadrature Formulas.
    In C. K. Chui, L. L. Schumaker (eds.): Approximation Theory IX, Vol. 1. Vanderbilt University Press, Nashville, TN (1998), 113-118. [Zbl. Math. 922.41016]
    Abstract

20. Existence and Construction of Definite Estimation Functionals.
    Studia Sci. Math. Hungar. 35 (1999), 217-236. [MR 2000a:41032; Zbl. Math. 959.41020]
    Abstract

21. (with A. D. Freed) On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity.
    In F. Keil, W. Mackens, H. Voß, J. Werther (eds.): Scientific Computing in Chemical Engineering II. Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties. Springer-Verlag, Heidelberg (1999), 217-224.
    Abstract

22. (with S. B. Damelin) Interpolatory Product Quadratures for Cauchy Principal Value Integrals with Freud Weights.
    Numer. Math. 83 (1999), 87-105. [MR 2000i:41037; Zbl. Math. 940.65023]
    Abstract and link to full text

23. (with A. D. Freed) The FracPECE Subroutine for the Numerical Solution of Differential Equations of Fractional Order.
    In S. Heinzel, T. Plesser (eds.): Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998. Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen (1999), 57-71.
    Abstract
    Full text (PDF file)

24. A Method for the Practical Evaluation of the Hilbert Transform on the Real Line.
    J. Comput. Appl. Math. 112 (1999), 45-53. [Zbl. Math. 944.65139]
    Abstract and link to full text

25. Estimation of Quadrature Errors in Terms of Caputo-Type Fractional Derivatives.
    Fract. Calc. Appl. Anal. 2 (1999), 313-327. [MR 2001j:41039]
    Abstract

26. (with P. Köhler) Asymptotic Behaviour of Fixed-Order Error Constants of Modified Quadrature Formulae for Cauchy Principal Value Integrals.
    J. Inequal. Appl. 5 (2000), 167-190. [MR 2000m:65037; Zbl. Math. 949.41019]
    Abstract and link to full text

27. (with K. Murawski) Randomly generated spectrum of the solar f-mode.
    Astronomy and Astrophysics 358 (2000), P 753-758.
    Abstract and link to full text

28. Two general methods for the numerical approximation of multidimensional Cauchy principal value integrals.
    ANZIAM J. 42 (2000), E1-E26. [MR 2001k:65046; Zbl. Math. 976.65025]
    Abstract and link to full text

29. (with S. B. Damelin) Boundedness and uniform numerical approximation of the weighted Hilbert transform on the real line.
    Numer. Funct. Anal. Optim. 22 (2001), 13-54. [MR 2002d:65151; Zbl. Math. 983.41015]
    Abstract and link to full text

30. (with N. J. Ford) Numerical Solution Methods for Distributed Order Differential Equations.
    Fract. Calc. Appl. Anal. 4 (2001), 531-542. [MR 2002k:65097]
    Abstract

31. (with N. J. Ford) Analysis of fractional differential equations.
    J. Math. Anal. Appl. 265 (2002), 229-248. [MR 2002m:34004; Zbl. Math. 1014:34003]
    Abstract and link to full text

32. (with N. J. Ford and A. D. Freed) A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations.
    Nonlinear Dynamics 29 (2002), 3-22. [MR 2003h:65085; Zbl. Math. 1009.65049]
    Abstract and link to full text

33. (with N. J. Ford) Numerical solution of the Bagley-Torvik equation.
    BIT 42 (2002), 490-507. [MR 2003i:65055]
    DOI: 10.1023/A:1021973025166
    Abstract and link to full text

34. Predictor-corrector strategies for single- and multi-term fractional differential equations.
    In E. A. Lipitakis (ed.): Proceedings of the 5th Hellenic-European Conference on Computer Mathematics and its Applications. LEA Press, Athens (2002), 117-122. [Zbl. Math. 1028.65081]
    Abstract

35. Efficient solution of multi-term fractional differential equations using P(EC)^mE methods.
    Computing 71 (2003), 305-319.
    Abstract and link to full text

36. (with M. Weilbeer) A numerical approach for Joulin's model of a point source initiated flame.
    Fract. Calc. Appl. Anal. 7 (2004), 191-212.
    Abstract

37. (with N. J. Ford and A. D. Freed) Detailed Error Analysis for a Fractional Adams Method.
    Numer. Algorithms 36 (2004), 31-52.
    Abstract and link to full text

38. Monotonicity Results for a Compound Quadrature Method for Finite-Part Integrals.
    J. Inequal. Pure Appl. Math. 5 (2004), article 44.
    Abstract and link to full text

39. (with N. J. Ford) Multi-order fractional differential equations and their numerical solution.
    Appl. Math. Comput. 154 (2004), 621-640.
    Abstract and link to full text

40. (with M. Weilbeer) Initial-boundary value problems for time-fractional diffusion-wave equations and their numerical solution.
    In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications. ENSEIRB, Bordeaux (2004), 551-557.
    Abstract

41. (with S. B. Damelin) Numerical approximation and stability of singular integral equations for Freud exponential weights on the line.
    J. Integral Equations Appl. 16 (2004), 273-292.
    Abstract and link to full text

42. A note on the midpoint rectangle formula for Riemann-Stieltjes integrals.
    J. Stat. Comput. Simulation 74 (2004), 920-922.
    Abstract

43. (with Y. Luchko) Numerical solution of linear multi-term initial value problems of fractional order.
    J. Comput. Anal. Appl. 6 (2004), 243-263.
    Abstract

44. (with S. B. Damelin) Weighted polynomial approximation and Hilbert transforms: Their connections to the numerical solution of singular integral equations.
    In Proceedings of the 4th International Conference on Dynamic Systems and Applications. Dynamic Publishers, Atlanta (2004), 20-26.
    Abstract

45. (with J. M. Ford, N. J. Ford and M. Weilbeer) A comparison of backward differentiation approaches for ordinary and partial differential equations of fractional order.
    In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Fractional Differentiation and its Applications. Ubooks, Neusäß (2005), 557-569.
    Abstract

46. (with A. D. Freed) Tensor fields for use in fractional-order viscoelasticity.
    In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Fractional Differentiation and its Applications. Ubooks, Neusäß (2005), 169-182.
    Abstract

47. (with N. J. Ford, A. D. Freed and Y. Luchko) Algorithms for the fractional calculus: A selection of numerical methods.
    Comput. Methods Appl. Mech. Eng. 194 (2005), 743-773.
    Abstract and link to full text

48. (with A. D. Freed) An efficient algorithm for the evaluation of convolution integrals.
    Computers Math. Applic., 51 (2006), 51-72.
    Abstract and link to full text

49. (with A. D. Freed) Fractional calculus in biomechanics: A 3D viscoelastic model using regularized fractional-derivative kernels with application to the human calcaneal fat pad.
    Biomechanics and Modeling in Mechanobiology, 5 (2006), 203-215.
    Abstract and link to full text

50. (with J. M. Ford, N. J. Ford and M. Weilbeer) Pitfalls in fast numerical solvers for fractional differential equations.
    J. Comput. Appl. Math. 186 (2006), 482-503.
    Abstract and link to full text

51. Smoothness Properties of Solutions of Caputo-type Fractional Differential Equations.
    Fract. Calc. Appl. Anal. 10 (2007), 151-160.
    Abstract

52. (with A. D. Freed) Caputo Derivatives in Viscoelasticity: A Non-linear Finite-deformation Theory for Tissue.
    Fract. Calc. Appl. Anal. 10 (2007), 219-248.
    Abstract

53. An Investigation of Some Nonclassical Methods for the Numerical Approximation of Caputo-Type Fractional Derivatives.
    Numer. Algorithms 47 (2008), 361-390.
    Abstract and link to full text

54. Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution.
    J. Europ. Syst. Autom. 42 (2008), 665-676.
    Abstract and link to full text

55. On the separation of solutions of fractional differential equations.
    Fract. Calc. Appl. Anal. 11 (2008), 259-268.
    Abstract

56. (with N. J. Ford) Numerical analysis for distributed-order differential equations.
    J. Comput. Appl. Math. 225 (2009), 96-104.
    Abstract and link to full text

57. An Improvement of a nonclassical numerical method for the computation of fractional derivatives.
    J. Vibration Acoustics 131 (2009), article 014502.
    Abstract and link to full text

58. (with M.-F. Danca) Fractional-order attractors synthesis via parameter switchings.
    Commun. Nonlinear Sci. Numer. Simul., to appear.
    Abstract and link to full text