حل شبه تحليلي معادله ديفرانسيل فازي پينليو

Quasi-Analytical Solution of the Painleve Fuzzy Differential Equation

در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﻌﺎدﻟﻪ دﯾﻔﺮاﻧﺴﯿﻞ ﭘﯿﻨﻠﯿﻮ ﻧﻮع اول را در ﻧﻈﺮ ﻣﯽﮔﯿﺮﯾﻢ ﮐﻪ ﻣﻘﺎدﯾﺮ ﺷﺮاﯾﻂ ﻣﺮزي در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﻘﺪار ﻓﺎزي ﻫﺴﺘﻨﺪ و ﻫﺪف ﻣﺤﺎﺳﺒﻪ ﺟﻮاب ﺗﻘﺮﯾﺒﯽ ﺑﺮاي آن ﻣﯽﺑﺎﺷﺪ. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر اﺑﺘﺪا ﺑﺎ اﺳﺘﻔﺎده از اﻋﻤﺎل ﺣﺴﺎﺑﯽ روي دادهﻫﺎي ﻓﺎزي، ﻣﻌﺎدﻟﻪ دﯾﻔﺮاﻧﺴﯿﻞ ﭘﯿﻨﻠﯿﻮ را ﺑﻪ ﺳﻪ دﺳﺘﮕﺎه ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﺑﺎ دادهﻫﺎي دﻗﯿﻖ ﺗﺒﺪﯾﻞ ﻣﯽﮐﻨﯿﻢ و در اداﻣﻪ ﺑﺎ اﺳﺘﻔﺎده از روش ﺗﻤﯿﻤﯽ و اﻧﺼﺎري )TAM(، ﺟﻮاب ﺗﻘﺮﯾﺒﯽ دﺳﺘﮕﺎه ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﺗﺒﺪﯾﻞ ﺷﺪه را ﻣﺤﺎﺳﺒﻪ و ﺑﻪ ﺟﻮاب ﺗﻘﺮﯾﺒﯽ ﻓﺎزي از ﻣﻌﺎدﻟﻪ دﯾﻔﺮاﻧﺴﯿﻞ ﭘﯿﻨﻠﯿﻮ ﻣﯽرﺳﯿﻢ. در ﭘﺎﯾﺎن ﺧﻄﺎ و ﻫﻤﮕﺮاﯾﯽ را ﺑﺎ ﯾﺎﻓﺘﻦ ﺟﻮاب ﺗﻘﺮﯾﺒﯽ ﻧﺸﺎن ﻣﯽدﻫﯿﻢ.

In this paper, we consider the first-order Painleve differential equation, which variables and coefficients are real but are known boundary conditions and fuzzy numbers. The goal is to calculate the approximate answer for it. Given the boundary conditions fuzzy, it is obvious that the approximate answer function must be a fuzzy function. For this purpose, first, by applying arithmetic on fuzzy data with three components of central index, left ambiguity and right ambiguity, it converts Painleve differential equation into three sets of differential equations (central index, left ambiguity and right ambiguity) with accurate data. do . Then, using the Tammy and Ansari (TAM) method, we calculate the approximate solution of each of the three transformed differential equations and arrive at the fuzzy approximate solution of the Painleve differential equation. Finally, by giving an example, we show the suitability of the method by calculating the error and convergence by finding the approximate solution.