SOLUTION OF HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH ALGEBRAIC COEFFICIENT BY FINITE DIFFERENCE EQUATIONS

Year 2004, Volume: 6 Issue: 1, 129 - 138, 01.01.2004

Seval Çatal

Abstract

There is no a general method for evaluating the implicit solutions of homogeneous
differential equations since they generally have individual properties. In this study, the
implicit solutions for some types of these differential equations are obtained by using finite
difference equations. The implicit solution obtained by reducing some differential equations
with algebraic coefficient to finite difference equations with constant coefficient is also
considered and numerical examples are presented

Keywords

Ordinary differential equations, Difference equation, Algebra tic equations.

CEBİRSEL KATSAYILI HOMOJEN DİFERANSİYEL DENKLEMLERİN FARK DENKLEMLERİ İLE ÇÖZÜMÜ

Abstract

Genel olarak, değişken katsayılı homojen diferansiyel denklemler, kendine has özellikler
içerdiklerinden kapalı çözümlerinin elde edilebilmeleri için genel bir yöntem yoktur. Bu
çalışmada bu tür diferansiyel denklemlerin bazı tiplerinin kapalı çözümleri fark denklemleri
kullanılarak elde edilmiştir. Ayrıca çalışmada bazı cebirsel katsayılı diferansiyel denklemlerin
sabit katsayılı fark denklemine indirgenmesi halinde elde edilen kapalı çözümü üzerinde
durulmuş ve sayısal örnekler sunulmuştur.

Keywords

Adi diferansiyel denklemler, Fark denklemi, Cebirsel denklemler

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