Bibliography for Newton-Cotes Integration

unabridged

 

  1. Newton-Cotes formulae for long-time integration
    Kalogiratou, Z.; Simos, T.E.
    Journal of Computational and Applied Mathematics, v 158, n 1, Sep 1, 2003, p 75-82, Compendex.
  2. Doubly Adaptive Quadrature Routines Based on Newton-Cotes Rules
    Espelid, T. O.
    Bit, 2003, vol. 43, no. 2, pp. 319-337, Ingenta.
  3. Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants
    Kreminski, R.
    Mathematics of Computation, 2003, vol. 72, no. 243, pp. 1379-1398, Ingenta.
  4. A study on the average case error of composite Newton-Cotes quadratures
    Choi, S. H.; Park, J. H.; Park, Y. Y.
    Journal of Applied Mathematics and Computing, 2003, vol. 12, no. 1/2, pp. 107-118, Ingenta.
  5. A unified approach to Newton-Cotes quadrature formulae
    El-Mikkawy, Moawwad
    Applied Mathematics and Computation (New York), v 138, n 2-3, Jun 20, 2003, p 403-413, Compendex.
  6. Erratum to "A Newton-Cotes quadrature approach for solving the aerosol coagulation equation" [Atmospheric Environment 36(3), 583-589]
    Sandu, A.
    Atmospheric Environment, 2002, vol. 36, no. 12, pp. 2081-2082, Ingenta.
  7. On the error analysis associated with the Newton-Cotes formulae
    El-Mikkawy MAE
    Int J Comput Math 79 (9): 1043-1047 2002, Web Of Science.
  8. A Newton-Cotes quadrature approach for solving the aerosol coagulation equation
    Sandu, A.
    Atmospheric Environment, v 36, n 3, 2002, p 583-589, Compendex.
  9. Understanding the Extra Power of the Newton-Cotes Formula for Even Degree (in Notes)  
    Kenneth J. Supowit  
    Mathematics Magazine, Vol. 70, No. 4. (Oct., 1997), pp. 292-293, Jstor.  
  10. Open Newton-Cotes differential methods as multilayer symplectic integrators.
    Chiou, J.C.; Wu, S.D.
    The journal of chemical physics, 1997, vol. 107, no. 17, pp. 6894, Ingenta.
  11. On the error and its control in a two-parameter generalised Newton-Cotes rule.   
    Ehrenmark, Ulf Torsten   
    J. Comput. Appl. Math. 75 (1996), no. 1, 171--195, MathSciNet.  
  12. Programmable incoherent Newton-Cotes optical integrator
    Ngo, Nam Q.; Binh, Le Nguyen
    Optics Communications, v 119, n 3-4, Sep 1, 1995, p 390-402, Compendex.
  13. On Gregory- and Modified Gregory-type Corrections to Newton-Cotes Quadrature.
    Bocher, P.; De Meyer, H.; Vanden Berghe, G.
    Journal of computational and applied mathematics, 1994, vol. 50, no. 1/3, pp. 145-158, Ingenta.
  14. Closed Newton-Cotes formulas
    Lecture Notes in Computer Science, n 848, 1994, p 70, Compendex.
  15. Open Newton-Cotes formulas
    Lecture Notes in Computer Science, n 848, 1994, p 73, Compendex.
  16. On Gregory- and modified Gregory-type corrections to Newton-Cotes quadrature.   
    Bocher, P.; De Meyer, H.; Vanden Berghe, G.    
    Proceedings of the Fifth International Congress on Computational and Applied Mathematics (Leuven, 1992), MathSciNet.  
  17. Numerical Evaluation of Line Integrals  
    K. Atkinson; E. Venturino  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 3. (Jun., 1993), pp. 882-888, Jstor.  
  18. Generating functions for Newton-Cotes formulae weights and error terms.   
    Brock, Bradley W.   
    Appl. Anal. 47 (1992), no. 2-3, 103--106, MathSciNet.  
  19. Numerical evaluation of general n-dimensional integrals by the repeated use of Newton-Cotes formulas.   
    Nihira, Takeshi; Iwata, Tadao  
    JAERI-M, 92-099. Japan Atomic Energy Research Institute, Ibaraki-ken, 1992. 28 pp, MathSciNet.  
  20. An explicit representation of the remainder of some Newton-Cotes formulas in terms of higher order differences.  
    Büttgenbach, B.; Lüttgens, G.; Nessel, R. J.  
    Z. Anal. Anwendungen 11 (1992), no. 1, 135--141, MathSciNet.  
  21. Modified Newton-Cotes Formulae for Numerical Quadrature of Oscillary Integrals with Two Independent Variable Frequencies.
    Van Daele, M.; De Meyer, H.; Vanden Berghe, G.
    International journal of computer mathematics, 1992, vol. 42, no. 1/2, pp. 83, Ingenta.
  22. On a generalization of compound Newton-Cotes quadrature formulas.
    Kohler, P.
    BIT, 1991, no. 3, pp. 540--54, Ingenta.
  23. A note on the Newton-Cotes integration formula.  
    Mills, T. M.; Smith, Simon J.  
    J. Approx. Theory 66 (1991), no. 1, 98--105, MathSciNet.  
  24. Estimating Integrals Using Quadrature Methods with an Application in Pharmacokinetics (in The Consultant's Forum)  
    A. John Bailer; Walter W. Piegorsch  
    Biometrics, Vol. 46, No. 4. (Dec., 1990), pp. 1201-1211, Jstor.  
  25. On a class of modified Newton-Cotes quadrature formulae based upon mixed-type interpolation.
    Vanden Berghe, G.; De Meyer, H.; Vanthournout, J.  
    Journal of computational and applied mathematics, 1990, vol. 31, no. 3, pp. 351-349, Ingenta.
  26. Closed Newton-Cotes quadrature rules for Stieltjes integrals and numerical convolution of life distributions.  
    Tortorella, Michael   
    SIAM J. Sci. Statist. Comput. 11 (1990), no. 4, 732--748, MathSciNet.  
  27. Newton-Cotes rules for triple integrals
    Sadiku, M. N. O; Kiem, Raymond Jong A.  
    Conference Proceedings - IEEE SOUTHEASTCON, v 2, 1990, p 471-475, Compendex.
  28. The Generating Function Method of Nonlinear Approximation  
    R. D. Small  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 1. (Feb., 1988), pp. 235-244, Jstor.  
  29. A remark on the Newton-Cotes formula. (Russian)  
    Natanson, G. I.  
    Metody Vychisl. No. 14 (1985), 58--59, 187, MathSciNet.  
  30. Improvements Of Adaptive Newton-Cotes Quadrature Methods.
    Ninomiya, Ichizo
    Journal of Information Processing, v 3, n 3, 1980, p 162-170, Compendex.
  31. On average Newton-Cotes quadrature formulas.   
    Omladic, M.  
    J. Inst. Math. Appl. 21 (1978), no. 4, 493--498, MathSciNet.  
  32. Exit Criteria for Newton-Cotes Quadrature Rules  
    J. H. Rowland, G. J. Miel  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1145-1150, Jstor.  
  33. Gegenbeispiel zum Newton-Cotes-Verfahren. (German)  
    Brass, H. Ein  
    Z. Angew. Math. Mech. 57 (1977), no. 10, 609, MathSciNet.  
  34. Generating and compounding product-type Newton-Cotes quadrature formulas.  
    Duris, Charles S.  
    ACM Transactions on Mathematical Software, v 2, n 1, Mar, 1976, p 50-58, Compendex.
  35. Some Comments on the Derivation and Structure of Newton-Cotes Quadrature Formulae  
    Ayse Alaylioglu,  G. A. Evans  and  J. Hyslop  
    Int. J. Math. Educ. Sci. Technol.,Vol. 5, (1974), pp. 213-217.   
  36. Monotonicity of Quadrature Approximations  
    D. J. Newman  
    Proceedings of the American Mathematical Society, Vol. 42, No. 1. (Jan., 1974), pp. 251-257, Jstor.  
  37. Norm Bounds of Quadrature Processes  
    Franz Locher  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 4. (Sep., 1973), pp. 553-558, Jstor.  
  38. Estimates of Upper Bounds for Quadrature Errors  
    J. D. Donaldson  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 1. (Mar., 1973), pp. 13-22, Jstor.  
  39. Quadraturformeln Vom Newton-Cotes-Typ Als Integrationsvorschrift Digitaler Integrieranlagen
    [Newton-Cotes Type Quadrature Formulas as Integration Provision of Digital Differential Analyzers]
    Lange, Otto  
    Angewandte Informatik/Applied Informatics, v 15, n 7, Jul, 1973, p 275-280, Compendex.
  40. Remainder terms of Newton-Cotes formulas in spectral form. (Russian)  
    Kunica, V. A.  
    Kibernetika (Kiev) 1972, no. 6, 112--120, MathSciNet.  
  41. Contribution to the numerical solution of differential equations by means of Runge-Kutta formulas with Newton-Cotes numbers weights.  
    Hut'a, Anton  
    Acta Fac. Rerum Natur. Univ. Comenian. Math. Publ. 28 (1972), 51--65, MathSciNet.  
  42. An analogue of the Newton-Cotes formulae for certain Cauchy type integrals and their principal values. (Russian)  
    Sokamolov, I.   
    Izv. Akad. Nauk Tad\v zik. SSR Otdel. Fiz.-Mat. i Geolog.-Him. Nauk 1972, no. 3(45), 6--13, 104, MathSciNet.  
  43. Addendum to "A Proof of the Newton-Cotes Quadrature Formulas with Error Term"  
    D. R. Hayes, L. Rubin  
    American Mathematical Monthly, Vol. 78, No. 9. (Nov., 1971), p. 988, Jstor.  
  44. Spectral effects in the use of Newton- Cotes approximations for computing discrete Fourier transforms
    Hunt B. R.
    IEEE Trans Comput, v C-20, n 8, Aug, 1971, p 942-3, Compendex.
  45. A Proof of the Newton-Cotes Quadrature Formulas with Error Term  
    D. R. Hayes, L. Rubin  
    American Mathematical Monthly, Vol. 77, No. 10. (Dec., 1970), pp. 1065-1072, Jstor.  
  46. Error of the Newton-Cotes and Gauss-Legendre Quadrature Formulas  
    N. S. Kambo  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 261-269, Jstor.  
  47. Newton-Cotes formulae in n-dimensions.  
    Guenther, R. B.; Roetman, E. L.  
    Numer. Math. 14 1969/1970 330--345, MathSciNet.  
  48. Newton-Cotes type quadrature formulas with terminal corrections.  
    Sack,R.A.  
    Comput.J.5 1962/1963 230--237, MathSciNet.  
  49. Newton-Cotes Quadrature Formulas (in Classroom Notes)  
    D. S. Greenstein  
    American Mathematical Monthly, Vol. 62, No. 7. (Aug. - Sep., 1955), pp. 487-488, Jstor.  
  50. A Note on Newton-Cotes Quadrature Formulas (in Classroom Notes)  
    Morris Morduchow  
    American Mathematical Monthly, Vol. 62, No. 1. (Jan., 1955), pp. 33-35, Jstor.  
  51. Approximate Product-Integration  
    Andrew Young  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 224, No. 1159. (Jul. 22, 1954), pp. 552-561, Jstor.  
  52. On the Expansion of the Remainder in the Open-Type Newton-Cotes Quadrature Formula  
    Orville G. Harrold, Jr.  
    American Journal of Mathematics, Vol. 59, No. 2. (Apr., 1937), pp. 275-289, Jstor.  
  53. On the Expansion of the Remainder in the Newton-Cotes Formula  
    J. V. Uspensky  
    Transactions of the American Mathematical Society, Vol. 37, No. 3. (May, 1935), pp. 381-396, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004