1,092
Views
4
CrossRef citations to date
0
Altmetric
Research Article

A novel scheme for the hyperbolic partial differential equation through Fibonacci wavelets

ORCID Icon &
Pages 1112-1132 | Received 25 Jun 2022, Accepted 31 Oct 2022, Published online: 11 Nov 2022

References

  • Strub I, Bayen A. Optimal control of air traffic networks using continuous flow model. (AIAA Conference on Guidance, Control, and Dynamics, Keystone, Colorado). 2006;3:1700–1710.
  • Bendahmane M, Nagaiah C, Comte É, et al. A 3D boundary optimal control for the bidomain-bath system modeling the thoracic shock therapy for cardiac defibrillation. J Math Anal Appl. 2016;437(2). hal-01261547.
  • Ng KW, Rohanin A. Numerical solution for PDE-constrained optimization problem in cardiac electrophysiology. Int J Comput Appl. 2012;44(12):11–15.
  • Martínez A, Rodríguez C, Vázquez M. Theoretical and numerical analysis of an optimal control problem related to wastewater treatment. SIAM J Control Optim. 2000;38(5):1534–1553.
  • Maidi A, Corriou J. Optimal control of nonlinear chemical processes using the variational iteration method. IFAC Symposium Advanced Control of Chemical Processes. 2012;45(15):898–903.
  • Bhatti MM, Zeeshan A, Bashir F, et al. Sinusoidal motion of small particles through a Darcy-Brinkman-Forchheimer microchannel filled with non-Newtonian fluid under electro-osmotic forces. J Taibah Univ Sci. 2021;15(1):514–529.
  • Tereshko D. Discrete optimization of unsteady fluid flows. CEUR Workshop Proc. 2016;1623:293–302.
  • Sadiya U, Inc M, Arefin MA, et al. Consistent travelling waves solutions to the non-linear time fractional Klein–Gordon and Sine-Gordon equations through extended tanh-function approach. J Taibah Univ Sci. 2022;16(1):594–607.
  • Munteanu I, Bratcu A, Cutululis N, et al. Optimal control of wind energy systems towards a global approach. Adv Ind Control. 2008.
  • Lenhart S, Workman JT. Optimal control applied to biological model. Math Comput Biol. 2007.
  • Gökmen E. A computational approach with residual error analysis for the fractional-order biological population model. J Taibah Univ Sci. 2021;15(1):218–225.
  • Gibson WC. The method of moments in electromagnetics. Abingdon: Taylor and Francis Group; 2008.
  • Pettersson MP, Iaccarino G, Nordström J. Polynomial chaos methods for hyperbolic partial differential equations: numerical techniques for fluid dynamics problems in the presence of uncertainties. Cham: Springer International Publishing; 2015.
  • Yeh KC, Liu CH. Wave propagation in random media in theory of ionospheric waves. Cambridge (MA): Academic Press. 1972;17:308–366.
  • Vergara RC. Development of geostatistical models using stochastic partial differential equations [Ph.D. thesis]. Paris: Université Paris Sciences et Lettres; 2018.
  • Atta AG, Abd-Elhameed WM, Moatimid GM, et al. Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations. Appl Numer Math. 2021;167:237–256.
  • Singh S, Patel VK, Singh VK. Application of wavelet collocation method for hyperbolic partial differential equations via matrices. Appl Math Comput. 2018;320:407–424.
  • Doha EH, Hafez RM, Youssri YH. Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations. Comp Math Appl. 2019;78:889–904.
  • Bhrawy AH, Hafez RM, Alzahrani EO, et al. Generalized Laguerre-Gauss-Radau scheme for the first order hyperbolic equations in a semi-infinite domain. Rom J Phys. 2015;60(7-8):918–934.
  • Tohidi E, Toutounian F. Convergence analysis of Bernoulli matrix approach for one-dimensional matrix hyperbolic equations of the first order. Comput Math Appl. 2014;68(1-2):1–12.
  • Shiralashetti SC, Kumbinarasaiah S. Laguerre wavelets collocation method for the numerical solution of the Benjamina–Bona–Mohany equations. J Taibah Univ Sci. 2019;13(1):9–15.
  • Shahni J, Singh R. Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet, and Laguerre-wavelet collocation methods. Math Comput Simul. 2022;194:430–444.
  • Shahni J, Singh R. Laguerre wavelet method for solving Thomas–Fermi type equations. Eng Comput. 2022;38:2925–2935.
  • Behera S, Ray SS. On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels. Comput Appl Math. 2022;41:211.
  • Guo L, Yu Z. A Gaussian wavelet-based method for extracting rockfall motion information in consecutive impact tests on flexible barrier systems. Int J Impact Eng. 2022;167:104264.
  • Gupta S, Ranta S. Legendre wavelet based numerical approach for solving a fractional eigenvalue problem. Chaos, Solitons Fractals. 2022;155:111647.
  • Kumbinarasaiah S, Raghunatha KR. Numerical solution of the Jeffery–Hamel flow through the wavelet technique. Heat Transfer. 2022;51:1568–1584.
  • Saeed U, Rehman MU. Hermite wavelet method for fractional delay differential equations. J Diff Equ. 2014;2014:359093.
  • Kumbinarasaiah S. A novel approach for multi-dimensional fractional coupled Navier–Stokes equation. SeMA; 2022.
  • Sezen C, Partal T. New hybrid GR6J-wavelet-based genetic algorithm-artificial neural network (GR6J-WGANN) conceptual-data-driven model approaches for daily rainfall–runoff modelling. Neural Comput Appl. 2022;34:17231–17255.
  • Janjarasjitt S. Comparison of wavelet-based decomposition and empirical mode decomposition of electrogastrogram signals for preterm birth classification. ETRI J. 2022: 1–11.
  • Adebayo TS. Environmental consequences of fossil fuel in Spain amidst renewable energy consumption: new insights from the wavelet-based Granger causality approach. Int J Sustain Dev World Ecol. 2022.
  • Ahsan M, Hussain I, Ahmad M. A finite-difference and Haar wavelets hybrid collocation technique for non-linear inverse Cauchy problems. Appl Math Sci Eng. 2022;30(1):121–140.
  • El-Gamel M, Mohamed N, Adel W. Numerical study of a nonlinear high order boundary value problems using Genocchi collocation technique. Int J Appl Comput Math. 2022;8:143.
  • Liu C, Yu Z, Zhang X, et al. An implicit wavelet collocation method for variable coefficients space fractional advection-diffusion equations. Appl Numer Math. 2022;177:93–110.
  • Sabermahani S, Ordokhani Y, Yousefi S. Fibonacci wavelets and their applications for solving two classes of time-varying delay problems. Optim Control Appl Methods. 2020;41:395–416.
  • Shah FA, Irfan M, Nisar KS, et al. Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions. Results Phys. 2021;24:104123.
  • Shiralashetti SC, Lamani L. Fibonacci wavelet based numerical method for the solution of nonlinear Stratonovich Volterra integral equations. Sci Afr. 2020;10:e00594.
  • Mohd I, Shah FA, Nisar KS. Fibonacci wavelet method for solving Pennes bioheat transfer equation. Int J Wavelets Multiresolut Inf Process. 2021;19(6):2150023.
  • Sabermahani S, Ordokhani Y. Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis. J Vib Control. 2021;27(15-16):1778–1792.
  • Kurt A, Yalçınbaş S, Sezer M. Fibonacci collocation method for solving high-order linear Fredholm integro-differential-difference equations. Int J Math Math Sci. 2013;2013:486013.
  • Alkan S, Cakmak M. Fibonacci collocation method for solving a class of systems of nonlinear differential equations. New Trends Math Sci. 2021;9(4):11–24.
  • Shiralashetti SC, Lamani L. A modern approach for solving nonlinear Volterra integral equations using Fibonacci wavelets. Electron J Math Anal Appl. 2021;9(2):88–98.
  • Irfan M, Shah FA. Fibonacci wavelet method for solving the time-fractional bioheat transfer model. Optik (Stuttg). 2021;241:167084.