Numerical Simulation of Nonlinear Schrödinger Equation in One and Two Dimensions
| Autor: | R. C. Mittal, Varun Joshi, Geeta Arora |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
010102 general mathematics
Basis function 01 natural sciences 010305 fluids & plasmas Computational Mathematics Nonlinear system symbols.namesake Exact solutions in general relativity Modeling and Simulation Ordinary differential equation 0103 physical sciences symbols Nyström method Applied mathematics 0101 mathematics Trigonometry Nonlinear Schrödinger equation Differential (mathematics) Mathematics |
| Zdroj: | Mathematical Models and Computer Simulations. 11:634-648 |
| ISSN: | 2070-0490 2070-0482 |
| DOI: | 10.1134/s2070048219040070 |
| Popis: | The present study aims to develop a hybrid scheme using trigonometric cubic B-spline basis functions with differential quadrature method for solving nonlinear Schrodinger equation in both one and two dimensions. This method reduces the nonlinear equation into a set of ordinary differential equations which can be further solved by the modified form of Ruge–Kutta method. This proposed method has been applied to this equation using two different approaches and also has been tested for proficiency on seven numerical examples. The obtained numerical results found to be synonymous when related with the exact solution. The obtained numerical results are also in good agreement with the results available in the literature. Comparison of numerical and the exact solution is depicted in the form of figures and tables. |
| Databáze: | OpenAIRE |
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