Approximated solution of First order Fuzzy Differential Equations under generalized differentiability

Abstract

<span style="background: white; color: #333333; line-height: 107%; font-family: 'Tahoma','sans-serif'; font-size: 9pt;">In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [</span><span style="background: white; color: #333333; line-height: 107%; font-family: 'Tahoma','sans-serif'; font-size: 9pt; mso-bidi-language: FA;" lang="FA" dir="RTL">۱</span><span style="background: white; color: #333333; line-height: 107%; font-family: 'Tahoma','sans-serif'; font-size: 9pt;">], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability.</span>