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    Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method
    (HINDAWI LTD, 2013) Eryilmaz, Aytekin; Atay, M. Tarik; Coskun, Safa B.; Basbuk, Musa
    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.
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    Magnus Expansion Method for Solving Singularly Perturbed Turning Point Problems Having Boundary Layers
    (AMER INST PHYSICS, 2015) Kome, Sure; Atay, Mehmet Tarik; Eryilmaz, Aytekin; Kome, Cahit; Simos, TE; Tsitouras, C
    In this paper, Magnus expansion method which is based on Lie groups and Lie algebras is presented to solve singularly perturbed boundary value problems having boundary layers. Numerical results are obtained by using different step sizes and small epsilon values which makes the problem stiff or nonstiff. In addition, maximum errors norms with L-infinity are tabulated in detail to show efficiency of the method.
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    Numerical Solutions of Linear and Nonlinear Lane-Emden Type Equations Magnus Expansion Method
    (AMER INST PHYSICS, 2015) Kome, Cahit; Atay, Mehmet Tarik; Eryilmaz, Aytekin; Kome, Sure; Simos, TE; Tsitouras, C
    In this paper, we study on the numerical solutions of linear and nonlinear singular initial value problems of Lane-Emden type with different orders of Magnus expansion method (MEM). The proposed method is different from other numerical techniques as it is based on lie groups and lie algebras. To show the efficiency of the method, we present approximate and exact values and also L-infinity error norms with detailed tables and figures.