A new method for solving initial value problems |
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| Affiliation: | 1. Department of Energy, Institute of Science and High Technology and Environmental Science, Graduate University of Advanced Technology, Kerman, Iran;2. Department of Chemical Engineering, University of South Carolina, Columbia, SC 29208, USA;1. Department of Metallurgy and Materials Science, Shahid Bahonar University, Kerman, Iran;2. Department of Material Engineering, Nanotechnology and Advanced Material Institute, Isfahan University of Technology (IUT), Isfahan, Iran;3. Department of Nanomaterials Engineering, Chungnam National University, Daejeon 305-764, Korea;1. State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China;2. Faculty of Chemistry, Northeast Normal University, Changchun 130024, China;3. Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada;1. Department of Mechanical Engineering, Shahrekord University, Shahrekord 88186-34141, Iran;2. Department of Mechanical Engineering, Lamerd Branch, Islamic Azad University, Lamerd, Iran;3. Parsian Gas Refining Company, Mohr, Iran |
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| Abstract: | A more accurate method (comparing to the Euler, Runge–Kutta, and implicit Runge–Kutta methods) for the numerical solutions of ordinary differential equations (ODEs) is presented in this paper. The coefficients in the approximate solution for the ODE using the proposed method are divided into two groups: the fixed coefficients and the free coefficients. The fixed coefficients are determined by using the same way as in the traditional Taylor series method. The free coefficients are obtained optimally by minimizing the error of the approximate solution in each time interval. Examples are presented to compare the numerical solutions of the Rahmanzadeh, Cai, and White's method (RCW) to those of other popular ODEs methods. |
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| Keywords: | Euler Runge–Kutta ODE |
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