519.6 Comparison of methods for calculating values special functions of mathematical physics

Апельцин В. Ф. (Bauman Moscow State Technical University), Krasnov I. K. (Bauman Moscow State Technical University)

SPECIAL FUNCTIONS, RECURRENT PROCEDURES, ASYMPTOTIC APPROXIMATION, NUMERICAL CALCULATION


doi: 10.18698/2309-3684-2020-4-111119


Comparison of two approaches to calculate values of Chebishev polynomials via recurrent procedures is realized. At that, first approach is based upon recursion upwards with respect to the index starting from the least index value. Second approach is based upon recursion downwards starting from evident asymptotical expressions of the functions with high values of index.


[1] Gradshtein I. S., Ryzhik I. M. Tablicy integralov, summ, ryadov i proizvedenii [Tables of integrals, sums, series and productions]. Moscow, Fizmatgiz Publ., 1962, 1100 p.
[2] Kuznecov D.S. Special'nye funkcii [Special functions]. Moscow, Vysshaya shkola Publ., 1962, 248 p.
[3] Campe de Ferrier J., Campbell R., Petyo G., Vogel T. Funkcii matematicheskoi fiziki: spravochnoe rukovodstvo [Functions of mathematical physics: a reference guide]. Moscow, Fizmatgiz Publ., 1963, 102 p.
[4] Vasiliev N., Zelevinsky A. Mnogochleny Chebysheva i rekurrentnye sootnosheniya [Chebyshev polynomials and recurrent relations]. Kvant — Quantum. 1982, no. 1, pp. 12–19.
[5] Vasiliev N.I., Klokov Yu.A., Shkerstena A.Ya. Primenenie polinomov Chebysheva v chislennom analize [Application of Chebyshev polynomials in numerical analysis]. Riga, Zinatne Publ., 1984, 240 p.
[6] Khovansky A.G. Polinomy Chebysheva i ih obrashchenie [Chebyshev polynomials and their conversion]. Matematicheskoe prosveshchenie — Mathematical Education, 2013, iss. 17, pp. 93–106.
[7] Frolov A.V., Tsvetkov V.I. On the harmonic analysis of functions of a real variable on a sphere. Computational Mathematics and Mathematical Physics, 2004, vol. 44, no. 11, pp. 1867–1874.
[8] Nagle R.K., Saff E.B., Snider A.D. Fundamentals of Differential Equations. Boston, Pearson Education Publ., 2012, 719 p.
[9] Reutskiy S.Y., Chen C.S. Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions. International Journal for Numerical Methods in Engineering, 2006, vol. 67, iss. 13, pp. 1811–1829.
[10] Tian H.Y. Reducing order of derivatives and derivation of coefficients for Chebyshev polynomial approximation. Preprint, 2006.
[11] Reutskiy S.Y., Chen C.S., Tian H.Y. A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conductions problems. International Journal for Numerical Methods in Engineering, 2008, vol. 74, iss. 10, pp. 1621–1644.
[12] Boyce W.E., Diprima R.C., Meade D.B. Elementary differential equations and boundary value problems. Hoboken, John Wiley & Sons Publ., 2017, 622 p.
[13] Ding J., Tian H.Y., Chen C.S. The recursive formulation of particular solutions for some elliptic pdes with polynomial source functions. Communications in Computational Physics, 2009, vol. 5, iss. 5, pp. 942–958.
[14] Krasnov I.K., Mozzhorina T.Yu., Balanin A.N. Numerical modeling of alloys nanostructure rearrangement by means of molecular dynamics methods. Маthematical Modeling and Computational Methods, 2017, no. 4, pp. 3–16.


Апельцин В.Ф., Краснов И.К. Сравнение методов вычисления значений специальных функций математической физики. Математическое моделирование и численные методы, 2020, № 4, с. 111–119



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