Different computational approach for Fourier transforms by using variational iteration method

Year 2022, Volume: 11 Issue: 3, 190 - 198, 31.12.2022

Ahmad Issa , Murat Düz

https://doi.org/10.54187/jnrs.1177925

Abstract

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.

Keywords

VIM, Fourier transform, Dirac delta function

References

• 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.