N‎umerical ‎q‎uasilinearization scheme ‎for the integral equation form of the Blasius equation

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran


‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎of ‎the ‎nonlinear ‎problem. ‎In ‎this ‎article, ‎using ‎some ‎transformations‎, ‎the ‎well-known ‎Blasius ‎equation ‎which ‎is a‎ ‎nonlinear ‎third ‎order ‎boundary ‎value ‎problem,‎ ‎is ‎converted ‎to a‎ ‎nonlinear ‎Volterra ‎integral ‎equation ‎satisfying ‎‎the ‎conditions ‎of ‎the ‎quasilinearization ‎scheme. ‎By applying the quasilinearization, ‎‎‎‎the‎ ‎solutions‎ of the ‎‎obtained ‎linear ‎integral ‎equations ‎are ‎approximated ‎by ‎the ‎collocation ‎method. ‎Employing‎ ‎the ‎inverse ‎of ‎the ‎‎transformation gives the approximation solution of the Blasius equation. ‎E‎rror analysis is performed and comparison of results with the other methods shows the priority ‎of ‎the ‎proposed ‎method.‎