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

Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:

JR_CMDE-12-4_007

تاریخ نمایه سازی: 8 مهر 1403

Abstract:

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.

Authors

Anshima Singh

Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, India.

Sunil Kumar

Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, India.

Higinio Ramos

Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamancay, ۳۷۰۰۸, Spain.