Ayrık Adomian ayrışım metodu ile kesirli mertebe fark denklemlerinin çözümü

Bu makalede, hem lineer hem de lineer olmayan kesirli mertebe kısmi fark denklemlerini çözmek için ayrık Adomian ayrışım metodunu(DADM) önerdik ve önerilen metodun uygulanabilirliğini göstermek için birkaç örnek verdik. Sonuçlar, DADM’nin etkili, doğru ve diğer kesirli mertebe fark denklemlerine uygulanabileceğini gösterdi.Abstract In this paper, we propose the discrete Adomian decomposition method(DADM) to solve linear as well as nonlinear fractional partial difference equations and provide few examples to illustrate the applicability of proposed method. The results show that DADM is efficient, accurate and can be applied to other fractional difference equation

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems

Iterative methods for solving Riccati differential equations

This work considers the approximate solution of the Riccati differential equations (RDEs). For ease of computation, the iterative methods applied are the Daftardar-Gejji and Jafari Method (DJM) and the Picard Iteration Method (PIM). The results obtained via the DJM are compared with those from PIM. The comparison shows that both methods are in agreement with the corresponding exact form. The Picard approach transforms the differential equation into an interconnected form; though, Lipschitz's criterion of consistency but satisfied