جستجوی مقالات مرتبط با کلیدواژه "taylor series" در نشریات گروه "مکانیک"

Taylor series method is a simple analytical method, which is accessible to all non-mathematician, has slow convergence. This paper develops a new Taylor series based numerical method to overcome the shortcoming of the Taylor series while maintaining its simplicity. Some examples are given, showing its reliability and efficiency. The proposed method is also proved to be extremely effective for initial value problems and boundary value problems. The method provides a universal approach to various highly non-linear problems, and it sheds a bright light on numerical theories for practical engineering applications.

This paper points out some errors based on the one-dimensional Taylor series for a multi-dimensional function that is used for robots manufacturing. It is argued that the proof of theorem 1 is not mathematically true, and consequently, the obtained results cannot be correct. In addition to this, the stability analysis presented in the paper does not address the saturated area properly. Therein, stability is analyzed separately in saturated and unsaturated operation areas. However, the stability of the closed-loop system may not be guaranteed through these separate analyses, since transitions from saturation area to unsaturated area and vice versa are neglected. This work is an extension of the above paper, based on the revised Taylor series and considering actuator saturation limit in both controller design and stability analysis.

In the present study, a modified time relaxed Monte Carlo (MTRMC) method is developed for numerical solution of the Boltzmann equation in rarefied regimes. Taylor series expansion is employed to obtain a generalized form of the Wild sum expansion and consequently the modified collision functions with fewer inter-molecular interactions are obtained. The proposed algorithm is applied on the lid-driven micro cavity flow with different lid velocities and the results for velocity and shear stress distributions are compared with those from the standard DSMC and TRMC methods. The comparisons show excellent agreement between the results of the MTRMC method with their counterparts from TRMC and DSMC methods. The present study illustrates appreciable improvement in the computational expense of the MTRMC method compared to those from standard TRMC and DSMC methods. The improvement is more pronounced compared to the standard DSMC method. It is observed that up to 56% reduction in CPU time is obtained in the studied cases.