Wavelet based algorithm for numerical study of \((1+2)\) -dimensional time fractional diffusion problems

Advances in Difference Equations

article

Ghafoor, Abdul¹  Haq, Sirajul²  Hussain, Manzoor³  Kumam, Poom⁴ 

[1] Institute of Numerical Sciences, Kohat University of Science and Technology;Faculty of Engineering Sciences, GIK Institute;Department of Humanities and Science, College of Aeronautical Engineering, National University of Science and Tecnology;Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT);KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)

关键词: Diffusion problems;    Two-dimensional Haar wavelets;    Caputo fractional derivative of constant order;    Finite differences;   

DOI  :  10.1186/s13662-020-02861-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

An effective and robust scheme is developed for solutions of two-dimensional time fractional heat flow problems. The proposed scheme is based on two-dimensional Haar wavelets coupled with finite differences. The time fractional derivative is approximated by an L1-formula while spatial part is approximated by two-dimensional Haar wavelets. The proposed methodology first converts the problem to a discrete form and then with collocation approach to a system of linear equations which is easily solvable. To check the efficiency of the scheme, two error norms, E∞ an Erms, have been computed. The stability of the scheme has been discussed which is an important part of the manuscript. It is also observed that the spectral radius of the amplification matrix satisfies a stability condition. From computation it is clear that computed results are comparable with the exact solution.

【 授权许可】

CC BY