A new approach to incorporate uncertainty into Euler's method

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Fuzzy set provides a powerful technique to introduce uncertainty into numerical methods. However, the computations of fuzzy sets often face difficult problems. This is due to non-applicability of common existing methods, severe overestimation in computation, or very high computational complexity. This paper proposes a new strategy to introduce uncertainty into Euler's method. It consists of two parts. First, we propose a new fuzzy version of Euler's method, which takes into account the dependency problem that arises in the classical Euler's method. Second, we perform optimisation technique to approximate the solution of differential equations with fuzzy initial values. This combination turns out to be a great tool to tackle uncertainty in any numerical method. One example is provided to show the capability of our proposed methods compared to the conventional fuzzy version of Euler's method proposed in the literature.

Original languageEnglish
Pages (from-to)2509-2520
Number of pages12
JournalApplied Mathematical Sciences
Volume4
Issue number49-52
Publication statusPublished - 2010

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Euler's method
Fuzzy sets
Uncertainty
Numerical methods
Fuzzy Sets
Numerical Methods
Computational complexity
Differential equations
Optimization Techniques
Computational Complexity
Differential equation

Keywords

  • Euler's method
  • Fuzzy initial value
  • Fuzzy set
  • Optimisation

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

A new approach to incorporate uncertainty into Euler's method. / Ahmad, M. Z.; Hasan, Mohammad Khatim.

In: Applied Mathematical Sciences, Vol. 4, No. 49-52, 2010, p. 2509-2520.

Research output: Contribution to journalArticle

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