New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

Abstract

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

“…Substituting the system of equation ( 38) into the systems of equation (37), we get Now, we define the recurrence relation from the systems of equation (40) as follows:…”

“…The main aim of this work is to apply the double Sumudu transform method coupled with the new iterative method (NIT) proposed by Daftardar-Gejji and Jafari in [33] to find an exact/approximate solution of the nonlinear coupled sine-Gordon equation. The new iterative method (NIM) has been extensively used by many researchers for the treatment of linear and nonlinear ordinary and partial differential equations of integer and fractional order (see [33][34][35][36][37]). The method converges to the exact solution if it exists through successive approximations.…”

The Revised NIM for Solving the Non-Linear System Variant Boussinesq Equations and Comparison with NIM

“…Many researchers used the NIM method in order to solve: fractional boundary value problems with Dirichlet boundary conditions using NIM", linear and nonlinear KleineGordon equations, and the system of linear differential equations [11e13]. Using NIM, "the approximate analytical solutions of the NewelleWhiteheadeSegel equation and solution of fractional gas dynamics and coupled Burger's equations" were solved [14,15] in addition to the solutions of Eigen value problems and Variational problems [16,17]. The NIM also contributed to "solving nonlinear Burger's equation and coupled Burger's equations, as well as solving modified Korteweg-de Vries (MKdV) System from three equations.…”

Zamansal-Kesirli Diferansiyel Fark Burger Denkleminin Sonlu Farklar Yöntemiyle Çözümü

“…Hence, due to the rapid development of fractional numerical methods, more and more publications are emerging. [Mohan and Deekshitulu, 2012;Cui, 2009;Hodzic-Zivanovic and Jovanovic, 2017;Yokus and Kaya, 2017;Rawashdeh, 2017;Al-luhaibi, 2015]…”