16771

16771

الگوريتم عددي براي حل معادلات ديفرانسيل مرتبه ي كسري به كمك ماتريس عملياتي توابع كلاهي تعميم يافته

كارشناسي ارشد

رياضي كاربردي ‐ آناليز عددي

آبان 1395

پروفسور خسرو مالك نژاد

رياضي

1395/12/07

1/1/1900 12:00:00 AM

Abstract In this thesis, we propose a numerical algorithm for solving linear an​d non linear fractionaldifferential equations based on constructed integer order an​d fractional order generalized hat functions operational matrices of integration. The linear an​d nonlinear fractional order differential equations are transformed into a system of algebraic equations by these matrices an​d these algebraic equations are solved through known computational methods. Further some numerical examples are given to illustrate an​d establish the accuracy an​d reliability of the proposed algorithm. The results obtained by using the scheme presented here, are in good agreement with the analytical solutions an​d numerical results presented elsewhere. This dissertation essentially based on reference. Keywords : Generalized hat functions, Fractional order generalized hat functions, operational matrix of integration, Block pulse functions, Fractional differential equations .