Zaman Değişkeninde Kesirli Türev İçeren Navier-Stokes Denklemlerinin Sayısal Çözümü

Abstract

In this study, Navier-Stokes equations with fractional derivate are solved according to time variable. To solve these equations, hybrid generalized differential transformation and finite difference methods are used in various subdomains. The aim of this hybridization is to combine the stability of the difference method and simplicity of the differential transformation method in use. It has been observed that the computational intensity of complex calculations is reduced and also discontinuity due to initial conditions can be overcome when the size increased in the study. The convergence of the time-dependent series solution is ensured by multi-timestepping method. This study has shown that the hybridization method is effective, reliable and easy to apply for solving such type of equations.

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

“…[27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations.…”

“…The analytical and numerical solutions for the nonlinear fractional differential equations have fundamental importance. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. The Gardner and Cahn-Hilliard equations are studied through distinct techniques such as reduced differential transform method, 34 the modified Kudryashov technique, 35 Adomian decomposition method (ADM), 36 improved (G ′ /G) − expansion method, 37 homotopy perturbation method (HPM), 26 residual power series method (RPSM), 22 and many others.…”