Araştırma Makalesi

Yıl 2019,
Cilt: 2 Sayı: 2, 61 - 71, 30.12.2019
### Öz

### Kaynakça

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Mohyud-Din, “Variational iteration method with an auxiliary parameter for solving Volterra’s population model,” Nonlinear Sci. Lett. A, vol. 8, no. 4, pp. 389–396, 2017. [14] C.W. Clenshaw and A.R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960) 197–205. [15] Sloan IH and Smith WE. Product integration with the Clenshaw-Curtis points: implementation and error estimates. Numerische Mathematik. 1980 Dec 1;34(4):387-401. [16] A. Iserles and S.P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. Royal Soc. A 461 (2005) 1383–1399. [17] H. Ahmad, “Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Fokker-Planck Equation,” Earthline J. Math. Sci., pp. 29–37, Apr. 2019. [18] H. Ahmad and T. A. Khan, “Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations,” J. Low Freq. Noise Vib. Act. Control, vol. 38, no. 3–4, pp. 1113–1124, Jan. 2019. [19] H. Ahmad and T. A. Khan, “Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems,” Noise Vib. Worldw., vol. 51, no. 1-2, pp. 12-20, 2020. [20] H. Ahmad, “Variational iteration algorithm-II with an auxiliary parameter and its optimal determination,” Nonlinear Sci. Lett. A, vol. 9, no. 1, pp. 62–72, 2018. [21] H. Ahmad, T. A. Khan, and C. Cesarano, “Numerical Solutions of Coupled Burgers′ Equations,” Axioms, vol. 8, no. 4, p. 119, Oct. 2019. [22] H. Ahmad, A. R. Seadawy, and T. A. Khan, “Numerical solution of Korteweg-de Vries-Burgers equation by the modified variational Iteration algorithm-II arising in shallow water waves,” Phys. Scr., Dec. 2019. DOI: 10.1088/1402-4896/ab6070. [23] H. Wang and S. Xiang, On the evaluation of Cauchy principal value integrals of oscillatory functions, J. Comput. Appl. Math. 234 (2010) 95–100. [24] H. Kang and S. Xiang, G. He, Computation of integrals with oscillatory and singular integrands using Chebyshev expansions. Journal of Computational and Applied Mathematics. 2013 Apr 1;242:141-56. [25] H. Kang and S. Xiang, Efficient quadrature of highly oscillatory integrals with algebraic singularities. Journal of Computational and Applied Mathematics. 2013 Jan 1;237(1):576-88. [26] S. Zaman and Siraj-ul-Islam, Efficient numerical methods for Bessel type of oscillatory integrals. Journal of Computational and Applied Mathematics. 2017 May 1;315:161-74. [27] A. L. Hascelik, Efficient computation of highly oscillatory Fourier-type integrals with monomial phase functions and Jacobi-type singularities. Applied Numerical Mathematics. 2019 Oct 16. [28] A. Al-Fhaid and S. Zaman, Meshless and wavelets based complex quadrature of highly oscillatory integrals and the integrals with stationary points. Engineering Analysis with Boundary Elements. 2013 Sep 1;37(9):1136-44. [29] I Aziz and W. Khan, Quadrature rules for numerical integration based on Haar wavelets and hybrid functions. Computers & Mathematics with Applications. 2011 May 1;61(9):2770- 81. [30] Siraj-ul-Islam and S. Zaman. New quadrature rules for highly oscillatory integrals with stationary points. Journal of Computational and Applied Mathematics. 2015 Apr 15;278:75-89.

Yıl 2019,
Cilt: 2 Sayı: 2, 61 - 71, 30.12.2019
### Öz

### Anahtar Kelimeler

### Kaynakça

In this paper, we design an accurate scheme for the approximation of highly oscillatory integrals having singularity . The interval of integration [a,b] is divided into two subintervals and then approximate the integral over first interval by hybrid function quadrature (Q_hf [g]), while for the approximation of integrals over the second interval we use Levin meshless method (Q_L^m [g]). For a result, we find the sum of both the integrals. To check the effectiveness of method results of some test problems are calculated by hybrid function quadrature and compared with the results produces by the proposed method.

oscillatort integral singularity Levin method hybrid fuction

Toplam 1 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Uygulamalı Matematik |

Bölüm | Makaleler |

Yazarlar | |

Yayımlanma Tarihi | 30 Aralık 2019 |

Kabul Tarihi | 2 Şubat 2020 |

Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 2 |

International Journal of Informatics and Applied Mathematics