دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,272
تعداد مقالات15,720
تعداد مشاهده مقاله51,824,640
تعداد دریافت فایل اصل مقاله14,664,519
Singh, Anshima, Kumar, Sunil, Ramos, Higinio. (1403). An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations. سامانه مدیریت نشریات علمی, 12(4), 719-740. doi: 10.22034/cmde.2024.57372.2398
Anshima Singh; Sunil Kumar; Higinio Ramos. "An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations". سامانه مدیریت نشریات علمی, 12, 4, 1403, 719-740. doi: 10.22034/cmde.2024.57372.2398
Singh, Anshima, Kumar, Sunil, Ramos, Higinio. (1403). 'An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations', سامانه مدیریت نشریات علمی, 12(4), pp. 719-740. doi: 10.22034/cmde.2024.57372.2398
Singh, Anshima, Kumar, Sunil, Ramos, Higinio. An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations. سامانه مدیریت نشریات علمی, 1403; 12(4): 719-740. doi: 10.22034/cmde.2024.57372.2398

An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations

Computational Methods for Differential Equations
مقاله 7، دوره 12، شماره 4، دی 2024، صفحه 719-740    اصل مقاله (2.29 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57372.2398
نویسندگان
Anshima Singh* 1؛ Sunil Kumar1؛ Higinio Ramos2
1Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, India.
2Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamancay, 37008, Spain.
چکیده
The primary objective of this research is to develop and analyze a robust computational method based on exponential B splines for solving fractional sub-diffusion equations. The fractional operator includes the Mittag-Leffler function of one parameter in the form of a kernel that is non-local and non-singular in nature. The current approach is based on an effective finite difference method for discretizing in time, and the exponential B-spline functions for discretizing in space. The proposed scheme is proven to be unconditionally stable and convergent. Also, the unique solvability of the method is established. Numerical simulations conducted for multiple test examples validate the agreement between the obtained theoretical results and the corresponding numerical outcomes.
کلیدواژه‌ها
Fractional sub-diffusion equation؛ Time fractional derivative؛ Exponential B-spline collocation؛ Stability analysis؛ Error bounds
مراجع
  • [1] M. N. Alam, H. S. Akash, U. Saha, M. S. Hasan, M. W. Parvin, and C. Tun, Bifurcation Analysis and Solitary Wave Analysis of the Nonlinear Fractional Soliton Neuron Model, Iranian Journal of Science, 47 (2023), 1797– 1808.
  • [2] M. N. Alam and S. M. R. Islam, The agreement between novel exact and numerical solutions of nonlinear models, Partial Differential Equations in Applied Mathematics, 8 (2023), 100584.
  • [3] T. Allahviranloo and B. Ghanbari, On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach, Chaos, Solitons & Fractals, 130 (2020), 109397.
  • [4] F. Amblard, A. C. Maggs, B. Yurke, A. N. Pargellis, and S. Leibler, Subdiffusion and anomalous local viscoelasticity in actin networks, Physical review letters, 77 (1996), 4470.
  • [5] I. Ardelean, G. Farrhera, and R. Kimmich, Effective diffusion in partially filled nanoscopic and microscopic pores, Journal of Optoelectronics and Advanced Materials, 9 (2007), 655.
  • [6] A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, arXiv preprint arXiv:1602.03408, (2016).
  • [7] E. Barkai, CTRW pathways to the fractional diffusion equation, Chemical Physics, 284 (2002), 13–27.
  • [8] C. D. Boor, A practical guide to splines, 27 (1978).
  • [9] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 73–85.
  • [10] Y. Cicek, N. G. Kaymak, E. Bahar, G. Gurarslan, and G. Tangolu, A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burgers equation, Computational Methods for Differential Equations, 11 (2023), 130–142.
  • [11] C. M. Chen, F. Liu, I. Turner, and V. Anh, A Fourier method for the fractional diffusion equation describing sub-diffusion, Journal of Computational Physics, 227 (2007), 886–897.
  • [12] A. Dokoumetzidis and P. Macheras, Fractional kinetics in drug absorption and disposition processes, Journal of pharmacokinetics and pharmacodynamics, 36 (2009), 165–178.
  • [13] R. Ghaffari and F. Ghoreishi, Reduced spline method based on a proper orthogonal decomposition technique for fractional sub-diffusion equations, Applied Numerical Mathematics, 137 (2019), 62–79.
آمار
تعداد مشاهده مقاله: 139
تعداد دریافت فایل اصل مقاله: 198


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب