Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DEVELOPMENT OF A NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING A FRACTIONAL DECAY MODEL

  • SAID AL KATHIRI (School of Mathematical Sciences, University Sains Malaysia) ;
  • EIHAB BASHIER (Faculty of Education and Arts, Sohar University) ;
  • NUR NADIAH ABD HAMID (Academic Services) ;
  • NORSHAFIRA RAMLI (School of Mathematical Sciences, Universiti Sains Malaysia)
  • Received : 2024.01.08
  • Accepted : 2024.03.19
  • Published : 2024.05.30
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Abstract

In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

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Acknowledgement

Financial support from Universiti Sains Malaysia's Graduate On Time Incentive with account number 1001/PMATHS/823233 is gratefully acknowledged.

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