An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written inMapleandMatlab.

In this paper, we give the definitions of quaternionic Smarandache curves in 3-dimensional Euclidean space 3 E and we investigate some differential geometric properties of these curves.

In this paper, we obtained some characterizations of timelike curves according to Bihop frame in Minkowski 3-space 3 1 E by using Laplacian operator and Levi-Civita connection. Furthermore we gave the general differential equations which characterize the timelike curves according to the Bishop Darboux vector and the normal Bishop Darboux vector.

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In this paper, the spacelike curves of constant breadth according to Bishop frame in Minkowski 3-space are studied. The differential equations characterizing the spacelike curves of constant breadth in E 3 1 are obtained. Furthermore, It is shown that the spacelike curves of constant breadth are connected with slant helix in Minkowski 3-space E 3 1 .