%0 Journal Article %T Convergence analysis of spectral Tau method for fractional Riccati differential equations %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Mokhtary, P. %A Ghoreishi, F. %D 2014 %\ 10/01/2014 %V 40 %N 5 %P 1275-1290 %! Convergence analysis of spectral Tau method for fractional Riccati differential equations %K Fractional Riccati differential equations‎ %K ‎Caputo derivative‎ %K ‎spectral Tau method‎ %R %X ‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given and rate of‎ ‎convergence is established in the weighted $L^2-$norm‎. ‎Numerical‎ ‎results are presented to confirm the high accuracy of the‎ ‎method‎. %U http://bims.iranjournals.ir/article_565_640b209b5b3935e605fe16785504abcc.pdf