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A meshless method for solving mKdV equation |
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| Authors: | Reza Mokhtari Majid Mohseni |
| Affiliation: | 1. Institut für theoretische Physik, ETH Zürich, Wolfgang-Paulistr. 27, CH-8093, Switzerland;2. Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE, United Kingdom;1. Department of Mathematics, Federal University of São Carlos (UFSCar), Brazil;2. Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany;3. Institute of Mathematics and Computer Science, University of Münster, Germany;1. Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA;2. Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA |
| Abstract: | A meshless method based on a global collocation with radial basis functions for the numerical solution of the modified Korteweg–de Vries (mKdV) equation is presented. Standard types of radial basis functions are applied in the method of collocation. The stability analysis of the method is dealt with using a linearized stability analysis. The method?s accuracy and efficiency are examined by the simulation of a single soliton and interaction of two solitary waves. The four invariants of the motion are evaluated to determine the conservation properties of the method. A comparison with some earlier reported results is also carried out. |
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