روشی جدید برای حل معادلات دیفرانسیل فازی از مرتبه n ام با استفاده از چند جمله ای درونیاب
محورهای موضوعی : آمار
الهام احمدی
1
(
گروه ریاضی ، واحد شهر قدس، دانشگاه آزاد اسلامی، تهران، ایران
)
نازنین احمدی
2
(
گروه ریاضی ، واحد ورامین-پیشوا، دانشگاه آزاد اسلامی، ورامین ،ایران
)
کلید واژه: numerical method, Generalized differentiability, Polynomial Interpolation, Fuzzy differntial equation,
چکیده مقاله :
روشی جدید برای حل معادلات دیفرانسیل فازی از مرتبه n ام با استفاده از چند جمله ای درونیاب با توجه به اهمیت نقش معادلات دیفرانسیل فازی در علوم و مهندسی در این مقاله ما روشی عددی برای حل معادله دیفرانسیل فازی از مرتبه n ام تحت مشتق تعمیم یافته را مورد بررسی قرار می دهیم. در این روش جواب معادله دیفرانسیل فازی توسط چندجمله ای فازی که به فرم یک قطعه ای چند جمله ای است در هر زیر بازه از بازه جواب تقریب زده می شود. در حالت خاص برای حل معادله دیفرانسیل فازی از مرتبه دوم با توجه به نوع مشتق پذیری چهار حالت در نظر گرفته می شود و سپس چند جمله ای فازی برای هر حالت ساخته می شود. درجه قطعه ای چند جمله ا ی ها در هر یک از زیر بازه های جواب از درجه ۲ می باشد. این روش توسط دو مثال از معادله دیفرانسیل فازی مرتبه ۲ تحت مشتق تعمیم یافته شرح داده شده است.
A new method for solving n-order fuzzy differential equation by using polynomial interpolationA new method for solving n-order fuzzy differential equation by using polynomial interpolationGiven the importance of the role of fuzzy differential equations in science and engineering,in this paper, we study a numerical method for solving N th order fuzzy differential equations under generalized differentiability. In this method a solution of fuzzy differential equation is approximated by fuzzy polynomial in the form of piece wise fuzzy polynomials in eachsub interval of interval solution. In special case, for solving second order fuzzy differential equation under generalized differentiability, according to the type of differentiability, four cases are considered, then fuzzy polynomial approximation in each cases for solving fuzzy differential equation were constructed. The order of the piece wise fuzzy polynomial in each sub interval of solution is two .Finally this method is illustrated by solving two second order fuzzy differentialequations under generalized differentiability.
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