Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

Ali Fareed Jameel, Hafed H Saleh, Amirah Azmi, Abedel-Karrem Alomari, Nidal Ratib Anakira, Noraziah Haji Man

Abstract


This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider the solution. Hence, there is a need to formulate new, efficient, more accurate techniques. This is the focus of this study: two approximate analytical methods-homotopy perturbation method (HPM) and the variational iteration method (VIM) is proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM. The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach for nonlinear TPFBVPs.

Keywords


Approximate analytical; methods; Fuzzy differential equations; Homotopy perturbation method; Two-point BVP; Variational iteration method

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DOI: http://doi.org/10.11591/ijece.v12i2.pp1916-1928

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International Journal of Electrical and Computer Engineering (IJECE)
p-ISSN 2088-8708, e-ISSN 2722-2578