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

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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