EĞİŞKEN KATSAYILI YÜKSEK MERTEBEDEN LİNEER COMPLEX DİFERANSİYEL DENKLEMLERİN DAİRESEL BİR BÖLGEDE POLİNOM ÇÖZÜMLERİ

Yıl 2009, Cilt: 25 Sayı: 1, 374 - 389, 01.02.2009

Mehmet Sezer Bekir Tanay Mustafa Gülsu

Öz

Bu çalışmada dairesel bir bölgede karışık koşullar altında değişken katsayılı yüksek mertebeden lineer complex diferansiyel denklemlerin Taylor matris yöntemi ile nümerik çözümlerinin bulunması amaçlanmıştır. Belirtilen yöntem denklemdeki fonksiyonların kesilmiş Taylor polinomlarının matris formlarının denklemde yerine konması esasına dayanır. Böylece denklem ve koşullar matris denklemine dönüştürülür. Bu denklemlerin çözümleri Taylor polinomlarının katsayılarını oluştururlar.Yöntemin uygulaması çeşitli örneklerle açıklanmış ve sonuçlar tartışılmıştır.

Anahtar Kelimeler

Taylor yaklaşımları, Complex diferansiyel denklemler, Taylor matris yöntemi

A POLYNOMIAL APPROACH FOR SOLVING HIGH-ORDER LINEAR COMPLEX DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS IN DISC

Öz

The purpose of this study is to give a Taylor matrix method for approximately solving the high-order linear complex differential equations with variable coefficients under the mixed conditions in a circular domain. The method is based on first taking the truncated Taylor expansions of the expressions in equation and then substituting their matrix forms into the given equation. Hence the differential equation and conditions are transformed to the matrix equations. The solution of these equations yields the unknown Taylor coefficients of the solution function. To illustrate the pertinent features of the method, examples are presented and results are compared

Anahtar Kelimeler

Taylor approximation, Complex differential equations, Taylor matrix method

Kaynakça

• Kanwal R.P., Liu K.C., A Taylor expansion approach for solving integral equations. Int. J.Math.Educ.Sci.Technol.,20(3), 411-414, 1989.
• Sezer M.,Taylor polynomial solution of Volterra integral equations. Int. J. Math. Educ. Sci. Technol., 25(5), 625-633, 1994.
• Sezer M., A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J.Math.Educ. Sci. Technol.,27(6), 821-834, 1996.
• Nas S.,Yalçınbaş S., Sezer M., A Taylor polynomial approach for solving high-order linear Fredholm integro- differential equations. Int. J.Math.Educ. Sci. Technol.,31(2), 213-225, 2000.
• Gulsu M., and Sezer M., The approximate solution of high order linear difference equation with variable coefficients in terms of Taylor polynomials, App1. Math. Compt.,168(1), 76-88, 2005.
• Sezer M. and Gulsu M., A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument, App1. Math. Compt.,171(1), 332-344, 2004.
• Gulsu M. and Sezer M., A method for the approximate solution of high order linear difference equation in terms of Taylor polynomials, Intern.J.Comput. Math., 82(5), 629-642, 2005.
• Spiegel M.R., Theory and Problems of Complex variables, McGraw-Hill Inc. NewYork 1972.
• Chiang Y.M. and Wang S., Oscillation results of certain-higher order linear differential equations with periodic cefficients in the complex plane, J. Math. Anal. Appl.,215, 560-576, 1997.
• Heittokongas J., Korhonen R. and Rattya J., Growth estimates for solutions, Ann. Acad. Sci. Fenn. Math., 29, 233-246, 2004.
• Ishizaki K.and Tohge K., On the complex oscillation of some linear differential equations, J. Math. Anal. Appl., 216, 503-517, 1997.
• Ahlfors L.V., Complex Analysis, McGraw-Hill Inc. 1996.
• Sezer M. and Gulsu M., Approximate solution of complex differential equations for a rectangular domain with Taylor collacation method, Applied Math. and Computation,177(2), 844-851, 2006.