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Different computational approach for Fourier transforms by using variational iteration method

Yıl 2022, , 190 - 198, 31.12.2022
https://doi.org/10.54187/jnrs.1177925

Öz

In this paper, we present another method for computing Fourier transforms of functions considering the Variational Iteration Method (VIM). Through our procedure, the Fourier transforms of functions can be calculated precisely and without reference to complex integration.

Kaynakça

  • J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167(1), (1998) 57-68.
  • J. H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics, 34(4), (1999) 699-708.
  • J. H. He, X. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons and Fractals, 29(1), (2006) 108-113.
  • M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, Variational Method in the Mechanics of solids, 33(5), (1978) 156-162.
  • A. M. Wazwaz, A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Computers and Mathematics with Applications, 41(10), (2001) 1237-1244.
  • M. Moghimi, F. S. A. Hejazi, Variational iteration method for solving generalized Burger-Fisher and Burger equations, Chaos, Solitons and Fractals, 33(5), (2007) 1756-1761.
  • H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford, London, 1947.
  • R. E. Kidder, Unsteady flow of gas through a semi infinite porous medium, Journal of Applied Mechanics, 27, (1957) 329-332.
  • M. Matinfar, M. Ghasemi, Application of variational iteration method to nonlinear heat transfer equations using He?s polynomials, International Journal of Numerical Methods for Heat & Fluid Flow, 23(3), (2013) 520-531.
  • A. Malvandi, D.D. Ganji, A general mathematical expression of amperometric enzyme kinetics using He's variational iteration method with Pade approximation, Journal of Electroanalytical Chemistry, 711, (2013) 32-37.
  • M. Gubes, A new calculation technique for the Laplace and Sumudu transforms by means of the variational iteration method, Mathematical Sciences, 13(1), (2019) 21-25.
  • L. Xu, E. W. Lee, Variational iteration method for the magnetohydrodynamic flow over a nonlinear stretching sheet, Abstract and Applied Analysis, 2013, (2013) Article ID: 573782, 1-5.
  • A. M. Wazwaz, The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients, Central European Journal of Engineering, 4(1), (2014) 64-71.
  • M. Düz, A. Issa, S. Avezov, A new computational technique for Fourier transforms by using the Differential transformation method, Bulletin of International Mathematical Virtual Institute, 12(2), (2022) 287-295.
  • M. D\" uz, Solution of complex differential equations by using Fourier transform, International Journal of Applied Mathematics, 31(1), (2018) 23-32.
  • B. Osgood, The Fourier transform and its applications, Lecture notes for EE, 2009.
  • N. Wheeler, Simplified production of Dirac delta function identities, Reed College, 1997.
  • A. Issa, N. Qatanani, A. Daraghmeh, Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations, Journal of Applied Mathematics, 2020, (2020) Article ID: 2360487, 1-13.
Yıl 2022, , 190 - 198, 31.12.2022
https://doi.org/10.54187/jnrs.1177925

Öz

Kaynakça

  • J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167(1), (1998) 57-68.
  • J. H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics, 34(4), (1999) 699-708.
  • J. H. He, X. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons and Fractals, 29(1), (2006) 108-113.
  • M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, Variational Method in the Mechanics of solids, 33(5), (1978) 156-162.
  • A. M. Wazwaz, A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Computers and Mathematics with Applications, 41(10), (2001) 1237-1244.
  • M. Moghimi, F. S. A. Hejazi, Variational iteration method for solving generalized Burger-Fisher and Burger equations, Chaos, Solitons and Fractals, 33(5), (2007) 1756-1761.
  • H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford, London, 1947.
  • R. E. Kidder, Unsteady flow of gas through a semi infinite porous medium, Journal of Applied Mechanics, 27, (1957) 329-332.
  • M. Matinfar, M. Ghasemi, Application of variational iteration method to nonlinear heat transfer equations using He?s polynomials, International Journal of Numerical Methods for Heat & Fluid Flow, 23(3), (2013) 520-531.
  • A. Malvandi, D.D. Ganji, A general mathematical expression of amperometric enzyme kinetics using He's variational iteration method with Pade approximation, Journal of Electroanalytical Chemistry, 711, (2013) 32-37.
  • M. Gubes, A new calculation technique for the Laplace and Sumudu transforms by means of the variational iteration method, Mathematical Sciences, 13(1), (2019) 21-25.
  • L. Xu, E. W. Lee, Variational iteration method for the magnetohydrodynamic flow over a nonlinear stretching sheet, Abstract and Applied Analysis, 2013, (2013) Article ID: 573782, 1-5.
  • A. M. Wazwaz, The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients, Central European Journal of Engineering, 4(1), (2014) 64-71.
  • M. Düz, A. Issa, S. Avezov, A new computational technique for Fourier transforms by using the Differential transformation method, Bulletin of International Mathematical Virtual Institute, 12(2), (2022) 287-295.
  • M. D\" uz, Solution of complex differential equations by using Fourier transform, International Journal of Applied Mathematics, 31(1), (2018) 23-32.
  • B. Osgood, The Fourier transform and its applications, Lecture notes for EE, 2009.
  • N. Wheeler, Simplified production of Dirac delta function identities, Reed College, 1997.
  • A. Issa, N. Qatanani, A. Daraghmeh, Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations, Journal of Applied Mathematics, 2020, (2020) Article ID: 2360487, 1-13.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ahmad Issa 0000-0001-7495-3443

Murat Düz 0000-0003-2387-4045

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Issa, A., & Düz, M. (2022). Different computational approach for Fourier transforms by using variational iteration method. Journal of New Results in Science, 11(3), 190-198. https://doi.org/10.54187/jnrs.1177925
AMA Issa A, Düz M. Different computational approach for Fourier transforms by using variational iteration method. JNRS. Aralık 2022;11(3):190-198. doi:10.54187/jnrs.1177925
Chicago Issa, Ahmad, ve Murat Düz. “Different Computational Approach for Fourier Transforms by Using Variational Iteration Method”. Journal of New Results in Science 11, sy. 3 (Aralık 2022): 190-98. https://doi.org/10.54187/jnrs.1177925.
EndNote Issa A, Düz M (01 Aralık 2022) Different computational approach for Fourier transforms by using variational iteration method. Journal of New Results in Science 11 3 190–198.
IEEE A. Issa ve M. Düz, “Different computational approach for Fourier transforms by using variational iteration method”, JNRS, c. 11, sy. 3, ss. 190–198, 2022, doi: 10.54187/jnrs.1177925.
ISNAD Issa, Ahmad - Düz, Murat. “Different Computational Approach for Fourier Transforms by Using Variational Iteration Method”. Journal of New Results in Science 11/3 (Aralık 2022), 190-198. https://doi.org/10.54187/jnrs.1177925.
JAMA Issa A, Düz M. Different computational approach for Fourier transforms by using variational iteration method. JNRS. 2022;11:190–198.
MLA Issa, Ahmad ve Murat Düz. “Different Computational Approach for Fourier Transforms by Using Variational Iteration Method”. Journal of New Results in Science, c. 11, sy. 3, 2022, ss. 190-8, doi:10.54187/jnrs.1177925.
Vancouver Issa A, Düz M. Different computational approach for Fourier transforms by using variational iteration method. JNRS. 2022;11(3):190-8.


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