...A. Jabbari; H. Kheiri; A. Yildirim Purpose The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods. Design/methodology/approach The obtained approximation by using...

...Praveen Kumar Gupta; A. Yildirim; K.N. Rai Purpose This purpose of this paper is to find the approximate analytical solutions of a multidimensional partial differential equation such as Helmholtz equation with space fractional derivatives α,β,γ (1<α...

...Syed Tauseef Mohyud‐Din; Ahmet Yıldırım; Sefa Anıl Sezer Purpose The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series...

... of the flow equation and for an iterative solution of the discrete systems are discussed. Ideas for further development of existing preconditioners are proposed, implemented and investigated numerically. Findings A two‐level preconditioning, consisting of a transformation of the original system...

..., and the inclination of the cavity, θ, on the flow characteristics and the existence ranges of the multiple solutions obtained. Design/methodology/approach The Navier‐Stokes equations were discretized by using a finite difference technique. The vorticity and energy equations were solved by the alternating...

...Y.C. LI This paper presents approximate analytical solutions for the diffusion problems of a cylindrical hole in an infinite medium and a slot in an infinite medium with properly prescribed boundary conditions and initial conditions. These solutions have much simpler forms than those of exact...