Homotopy Analysis Method (HAM) is applied to find the critical buckling load of the Euler columns with continuous elastic restraints. HAM has been successfully applied to many linear and nonlinear, ordinary and partial, differential equations, integral equations, and difference equations. In this study, we presented the application of HAM to the critical buckling loads for Euler columns with five different support cases continuous elastic restraints. The results are compared with the analytic solutions.

Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

Hassas Nokta Konumlama (PPP) yöntemi, gerçek zamanlı (RT-PPP) ve ölçü sonrası değerlendirme (PP-PPP) olmak üzere iki şekilde uygulanmaktadır. Bu çalışmada, jeomanyetik aktivitelerin GNSS gözlemleri üzerindeki bozucu etkisinin sonuçlara yansımaması amacıyla Kp, Dst

Most of the phenomena of various fields of applied sciences are nonlinear problems. Recently, various types of analytical approximate solution techniques were introduced and successfully applied to the nonlinear differential equations. One of the aforementioned techniques is the Homotopy analysis method (HAM). In this study, we applied HAM to find critical buckling load of a column under end load dependent on direction. We obtained the critical buckling loads and compared them with the exact analytic solutions in the literature.

M any phenomena in science and engineering involve nonlinear problems. However, the majority of these nonlinear problems have no exact analytical solutions since it is generally dicult to solve nonlinear equations analytically. In recent years, these nonlinear equations have been solved by analytical approximate solution techniques, such as perturbation and nonperturbation techniques. Perturbation techniques usually depend on small/ large physical parameters. Although nonperturbation techniques do not depend on small/ large physical parameters, these methods cannot ensure the convergence of the solution series. In fact, neither perturbation methods nor nonperturbation techniques can adjust or control the convergence region and the rate of the approximation series. On the other hand, the homotopy analysis method (HAM) which is proposed by Liao [1, 2] is an analytic approach to obtain series solution of various types of linear and nonlinear differential equations, such as ordinary differential equations, partial differential equations, integro-differential equations, difference equations, differential-difference equations, integrodifferential difference equations [1, 2, 3, 4, 5, 6] and it provides a convenient way to adjust and control the Article History: