Yiğit Aksoy

New perturbation-iteration solutions for Bratu-type equations

Perturbation-iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation-iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation-iteration algorithms, new solutions of Bratu-type equations are obtained. Solutions constructed using different perturbation-iteration algorithms are contrasted with each other as well as with numerical solutions. It is found that algorithms with more Taylor series expansion terms yield more accurate results.

Perturbation-Iteration Method for First-Order Differential Equations and Systems

The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good agreement is found. The method can be applied to differential equation systems with success.

Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid

Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.

Group-Theoretic Approach to Boundary Layer Equations of an Oldroy-B Fluid

Boundary layer equations are derived for the first time for an Oldroy-B fluid. The symmetry analysis of the equations is performed using Lie Group theory and the partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved for the case of the stretching sheet problem. Effects of non-Newtonian parameters on the solutions are discussed.

Boundary Layer Theory and Symmetry Analysis of a Williamson Fluid

Boundary layer equations are derived for the first time for a Williamson fluid. Using Lie group theory, a symmetry analysis of the equations is performed. The partial differential system is transferred to an ordinary differential system via symmetries, and the resulting equations are numerically solved. Finally, the effects of the non-Newtonian parameters on the solutions are discussed

Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

Abstract Steady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.

Perturbation iteration method solutions of a nonlinear fin equation

Recently developed perturbation iteration method is successfully applied to a nonlinear fin equation. Approximate solutions are obtained using the perturbation iteration method as well as the classical perturbation method. Solutions obtained from the classical and the perturbation iteration method are compared with the numerical solutions. Perturbation iteration method yields very accurate results whereas the classical perturbation method fails to produce acceptable results for large parameters of perturbation.