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Sabermahani, Sedigheh, Ordokhani, Yadollah, Agarwal, Praveen. (1403). Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations. سامانه مدیریت نشریات علمی, 13(2), 450-465. doi: 10.22034/cmde.2024.59007.2503
Sedigheh Sabermahani; Yadollah Ordokhani; Praveen Agarwal. "Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations". سامانه مدیریت نشریات علمی, 13, 2, 1403, 450-465. doi: 10.22034/cmde.2024.59007.2503
Sabermahani, Sedigheh, Ordokhani, Yadollah, Agarwal, Praveen. (1403). 'Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations', سامانه مدیریت نشریات علمی, 13(2), pp. 450-465. doi: 10.22034/cmde.2024.59007.2503
Sabermahani, Sedigheh, Ordokhani, Yadollah, Agarwal, Praveen. Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations. سامانه مدیریت نشریات علمی, 1403; 13(2): 450-465. doi: 10.22034/cmde.2024.59007.2503

Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations

Computational Methods for Differential Equations
مقاله 7، دوره 13، شماره 2، خرداد 2025، صفحه 450-465    اصل مقاله (2.14 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.59007.2503
نویسندگان
Sedigheh Sabermahani1؛ Yadollah Ordokhani* 1؛ Praveen Agarwal2
1Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
21.Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajesthan, India. 2. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE. 3. International Center for Basic and Applied Sciences, Jaipur, 302029, India.
چکیده
This manuscript provides an efficient technique for solving time-fractional diffusion-wave equations using general Lagrange scaling functions (GLSFs). In GLSFs, by selecting various nodes of Lagrange polynomials, we get various kinds of orthogonal or non-orthogonal Lagrange scaling functions. The general Riemann-Liouville fractional integral operator (GRLFIO) of GLSFs is obtained generally. General Riemann-Liouville fractional integral operator of the general Lagrange scaling function is calculated exactly using the Hypergeometric functions. The operator extraction method is precisely calculated and this has a direct impact on the accuracy of our method. The operator and optimization method are implemented to convert the problem to a set of algebraic equations. Also, error analysis is discussed. To demonstrate the efficiency of the numerical scheme, some numerical examples are examined.
کلیدواژه‌ها
Time-fractional diffusion-wave equation؛ General Riemann-Liouville pseudo-operational matrix؛ Optimization method؛ General Lagrange scaling function
مراجع
  • [1] P. Akhavan, N. A. Ebrahim, and M. A. Fetrati, Major trends in knowledge management research: a bibliometric study, Scientometrics, 107(3) (2016), 1249-1264.
  • [2] A. H. Bhrawy, E. H. Doha, D. Baleanu, and S. S. Ezz-Eldien, A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations, Journal of Computational Physics, 293 (2015), 142-156.
  • [3] M. Dehghan, M. Abbaszadeh, and A. Mohebbi, Analysis of a meshless method for the time fractional diffusionwave equation, Numerical algorithms, 73(2) (2016), 445-476.
  • [4] M. Dehghan, M. Safarpoor, and M. Abbaszadeh, Two high-order numerical algorithms for solving the multiterm time fractional diffusion-wave equations, Journal of Computational and Applied Mathematics, 290 (2015), 174-195.
  • [5] R. Du, W. R. Cao, and Z. Z. Sun, A compact difference scheme for the fractional diffusion-wave equation, Applied Mathematical Modelling, 4(10) (2010), 2998-3007.
  • [6] A. Esen, Y. Ucar, N. Yagmurlu, and O. Tasbozan, A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations, Mathematical Modelling and Analysis, 18(2) (2013), 260-273.
  • [7] Z. Foroozandeh and M. Shamsi, Solution of nonlinear optimal control problems by the interpolating scaling functions, Acta Astronautica, 72 (2012), 21-26.
  • [8] H. Hajinezhad and A. R. Soheili, A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach, Computational Methods for Differential Equations, 11 (2023), 716-726.
  • [9] M. H. Heydari, M. R. Hooshmandasl, F. M. Ghaini, and C. Cattani, Wavelets method for the time fractional diffusion-wave equation, Physics Letters A, 379(3) (2015), 71-76.
  • [10] F. Liu, M. M. Meerschaert, R. J. McGough, P. Zhuang, and Q. Liu, Numerical methods for solving the multi-term time-fractional wave-diffusion equation, Fractional Calculus and Applied Analysis, 16(1) (2013), 9-25.
  • [11] R. Metzler and J. Klafter, The random walks guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, 339 (2000), 1-77.
  • [12] H. Mohammadi Firouzjaei, H. Adibi, and M. Dehghan, Local discontinuous Galerkin method for distributedorder timefractional diffusionwave equation: Application of Laplace transform, Mathematical Methods in the Applied Sciences, 44(6) (2021), 4923-4937.
  • [13] S. Nemat and S. Sedaghat, Matrix method based on the second kind Chebyshev polynomials for solving time fractional diffusion-wave equations, Journal of Applied Mathematics and Computing, 51 (2016), 189-207.
  • [14] R. R. Nigmatullin, To the theoretical explanation of the universal response, Physics of the Solid State B123 (1984), 739-745.
  • [15] F. Nourian, M. Lakestani, S. Sabermahani, and Y. Ordokhani, Touchard wavelet technique for solving timefractional Black-Scholes model, Computational and Applied Mathematics, 41(4) (2022), 150.
  • [16] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • [17] K. Rabiei and M. Razzaghi, A new numerical method for solving problems in fractional differential equations by using Mott wavelets, In 2022 Virtual Joint Mathematics Meetings (JMM 2022), AMS.
  • [18] K. Rabiei and M. Razzaghi, An approach to solve fractional optimal control problems via fractional-order Boubaker wavelets, Journal of Vibration and Control, 29(7-8) (2023), 1806-1819.
  • [19] K. Rabiei and M. Razzaghi, Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations, Applied Numerical Mathematics, 168 (2021), 221-234.
  • [20] S. Sabermahani and Y. Ordokhani, Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis, Journal of Vibration and Control, 27(15-16) (2021), 1778-1792.
  • [21] S. Sabermahani, Y. Ordokhani, and S. A. Yousefi, Fractional-order general Lagrange scaling functions and their applications, BIT Numerical Mathematics, 60 (2020), 101-128.
  • [22] S. Sabermahani, Y. Ordokhani, and S. A. Yousefi, Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations, Computational and Applied Mathematics, 37 (2018), 3846-3868.
  • [23] M. So, J. Kim, S. Choi, et al., Factors affecting citation networks in science and technology: focused on non-quality factors, Quality & Quantity, 49(4) (2015), 1513-1530.
  • [24] F. Soltani Sarvestani, M. H. Heydari, A. Niknam, and Z. Avazzadeh, A wavelet approach for the multi-term time fractional diffusion-wave equation, International Journal of Computer Mathematics, 96(3) (2019), 640-661.
  • [25] Z. Z. Sun and X. Wu, A fully discrete difference scheme for a diffusion-wave system, Applied Numerical Mathematics, 56(2) (2006), 193-209.
  • [26] S. Taherkhani, I. Najafi Khalilsaraye, and B. Ghayebi, A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations, Computational Methods for Differential Equations, 11(2) (2023), 357-368.
  • [27] S. Tavan, M. Jahangiri Rad, A. Salimi Shamloo, and Y. Mahmoudi, A numerical scheme for solving time-fractional Bessel differential equations, Computational Methods for Differential Equations, 10(4) (2022), 1097-1114.
  • [28] F. Yang, Y. Zhang, X. Liu, et al., The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation. Acta Mathematica Scientia, 40 (2020), 641-658.
  • [29] F. Zhou and X. Xu, Numerical solution of time-fractional diffusion-wave equations via Chebyshev wavelets collocation method, Advances in Mathematical Physics, 2017 (2017).
 

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