• International journal of advanced smart convergence
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• v.2 no.1
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• pp.18-20
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• 2013

The significance, is to introduce a novel way to employ the improved Runge-Kutta fifth order five stage method, here after called as Modified IRK(5,5) method, for system of second order robot arm problem and variations in angles at the joints in which parameters governing with two degrees of freedom which requires lesser number of function evaluations per time step as compared to the existing ones, in order to save time and spaceAn ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.

• Mass Spectrometry Letters
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• v.6 no.3
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• pp.59-64
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• 2015

Quadrupole ion trap mass analyzer with a simplified geometry, namely, the cylindrical ion trap (CIT), has been shown to be well-suited using in miniature mass spectrometry and even in mass spectrometer arrays. Computation of stability regions is of particular importance in designing and assembling an ion trap. However, solving CIT equations are rather more difficult and complex than QIT equations, so, analytical and matrix methods have been widely used to calculate the stability regions. In this article we present the results of numerical simulations of the physical properties and the fractional mass resolutions m/Δm of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) at the optimum radius size for both ion traps. Because of similarity the both results, having determining the optimum radius, we can make much easier to design CIT. Also, the simulated results has been performed a high precision in the resolution of trapped ions at the optimum radius size.

• Journal of computational fluids engineering
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• v.13 no.3
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• pp.69-78
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• 2008

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

• Membrane Journal
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• v.16 no.3
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• pp.204-212
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• 2006

A numerical analysis was carried out for separation of carbon dioxide from carbon dioxide/nitrogen gas mixture by a polyethersulfone hollow fiber membrane which has shown a good stability against plasticization by carbon dioxide and an excellent separation efficiency fur carbon dioxide from its gas mixture. A computer program for carbon dioxide separation was developed using the Compaq Visual Fortran 6.6 software. Governing module equations were thought to be an initial-value problem and the nonlinear ordinary differential equations were simultaneously solved using the Runge-Kutta-Verner fifth-order method. From results of numerical analysis, the carbon dioxide partial pressure of the feed stream, the pressure ratio of the feed side to the permeate side and the feed gas residence time at the inside of a membrane were found to be very important factors to affect the permeation characteristics of carbon dioxide.

• Advances in aircraft and spacecraft science
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• v.8 no.4
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.