یک روش بدون شبکۀ محلی به‌صورت قوی برای حل معادلۀ شرودینگر وابسته به زمان دوبعدی

1. Torres-Vega G., Frederick J., "Quantum mechanics in phase space: New approaches to the correspondence principle", Chem. Phys, 93 (12) (1990) 8862-8874. 2. Jazbi B., Moini M., "On the numerical solution of one dimensional Schr¨odinger equation with boundary conditions involving fractional differential operators", IUST International Journal of Engineering Science, 19 (2008) 21-26. 3. Bourgain J., "Global solution of nonlinear Schr¨odinger equations", Amer. Math. Soc. Colloq. Publ., (1999). 4. Sulem C., Sulem P. L., "The Nonlinear Schr¨odinger Equation: Self-Focusing and Wave Collapse", Springer, New York, (1999). 5. Sulem P. L., Sulem C., Patera A., "Numerical Simulation of Singular Solutions to the Two-Dimensional Cubic Schr¨odinger Equation", Communications on Pure and Applied Mathematics, 37 (1984) 755-778. 6. Sacchetti A., "Nonlinear time-dependent Schr¨odinger equations: The Gross-Pitaevskii equation with double-well potential", Evol. Equ., 4 (2004) 345-369. 7. Gao Z., Xie S., "Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schr¨odinger equations", Applied Numerical Mathematics, 61 (4) (2011) 593-614. 8. Bao W., Shen J., "A fourth-order time-splitting Lagurre-Hermite pseudo-spectral method for Bose Einstein condensates", SIAM. Sci. Comput., 26 (2005) 2010-2028. 9. Kalita J., Chhabra P., Kumar S., "A semi-discrete higher order compact scheme for the unsteady two-dimensional Schr¨odinger equation", Computational Applied Mathematics, 197 (2006) 141-149. 10. Xie S., Li G., Yi S., "Compact finite difference schemes with high accuracy for one- dimensional nonlinear Schr¨odinger equation", Comput. Methods Appl. Mech. Engrg., 198 (2009) 1052-1060. 11. Dehghan M., Mirzaei D., "Numerical solution to the unsteady two-dimensional Schr¨odinger equation using meshless local boundary integral equation method", Int. J. Numer. Meth. Engng, 76 (2008) 501-520. 12. Dehghan M., Taleei A., "A chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schr¨odinger equations", Computer Physics Communications, 182 (12) (2011) 2519-2529. 13. Mohebbi A., Dehghan M., "The use of compact boundary value method for the solution of two-dimensional Schr¨odinger equation", Journal of Computational and Applied Mathematics, 225 (1) (2009) 124 -134. 14.Abbasbandy S., Ghehsareh H. R., Hashim I., "A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation", Eng. Anal. Bound. Elem., 37 (6) (2013) 885-898. 15. Ismail M., "Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method", Mathematics and Computers in Simulation, 78 (4) (2008) 532-547. 16. Xu Y., Zhang L., "Alternating direction implicit method for solving two-dimensional cubic nonlinear Schr¨odinger equation", Computer Physics Communications, 183 (5) (2012) 1082-1093. 17. Abbasbandy S., Shirzadi A., "MLPG method for two-dimensional diffusion equation with Neumann’s and non-classical boundary conditions", Appl. Numer. Math., 61 (2011) 170-180. 18. Abbasbandy S., Sladek V., Shirzadi A., Sladek J., "Numerical simulations for coupled pair of diffusion equations by MLPG method", CMES Compt. Model. Eng. Sci., 71 (1) (2011) 15-37. 19. Shirzadi A., Ling L., "Convergent overdetermined-RBF-MLPG for solving second order elliptic PDEs", Advances in Applied Mathematics and Mechanics, 5 (1) (2013) 78-89. 20. Shirzadi A., Sladek V., Sladek J., "A local integral equation formulation to solve coupled nonlinear reaction-diffusion equations by using moving least square approximation", Eng. Anal. Bound. Elem., 37 (1) (2013) 8-14. 21. Shirzadi A., Ling L., Abbasbandy S., "Meshless simulations of the two-dimensional fractional-time convection-diffusion-reaction equations", Eng. Anal. Bound. Elem., 36 (2012) 1522-1527. 22. Shirzadi A., Sladek V., Sladek J., "A meshless simulations for 2d nonlinear reaction- diffusion brusselator system", CMES: Computer Modeling in Engineering & Sciences, 95 (4) (2013) 259-282. 23. Shirzadi A., "Numerical simulations of 1D inverse heat conduction problems using over-determined RBF-MLPG method", Communications in Numerical Analysis, (2013). 24. Shirzadi A., "Meshless local integral equations formulation for the 2D convection- diffusion equations with a nonlocal boundary condition"”, Computer Modeling in Engineering & Sciences (CMES), 85 (1) (2012) 45-63. 25. Rad J. A., Parand K., Abbasbandy S., "Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate european and american options", Communications in Nonlinear Science and Numerical Simulation, 22 (13) (2015) 1178-1200. 26. Shirzadi A., Takhtabnoos F., "A local meshless collocation method for solving Landau Lifschitz -Gilbert equation", Eng. Anal. Bound. Elem., 61 (2015) 104-113. 27. Shirzadi A., Takhtabnoos F., "A local meshless method for cauchy problem of elliptic pdes in annulus domains", Inverse Problems in Science and Engineering, 0 (0) (2015) 1-15. URL http://dx.doi.org/10.1080/17415977.2015.1061521 28. Shirzadi A., "Numerical solutions of 3D cauchy problems of elliptic operators in cylindrical domain using local weak equations and radial basis functions", International Journal of Computer Mathematics, 0 (0) (0) 1-11. URL http://dx.doi.org/10.1080/00207160.2015.1104305. 29.Lee C. K., Liu X., Fan S. C., "Local multiquadric approximation for solving boundary value problems", Computational Mechanics, 30 (2003) 396-409. 30. Stevens D., Power H., Meng C., Howard D., Cliffe K., "An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions", Journal of Computational Physics, 254 (0) (2013) 52-75. 31. Cai X., Sun X., Li Z., Ji G., Lu J., "The Element-Free Galerkin Method for Two- dimensional Schr¨odinger Equation", Procedia Engineering,31 (0) (2012) 1108-1114, international Conference on Advances in Computational Modeling and Simulation. 32. Dehghan M., "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices", Mathematics and Computers in Simulation, 71 (1) (2006) 16-30. 33. Dehghan M., Shokri A., "A numerical method for two-dimensional Schr¨odinger equation using collocation and radial basis functions", Computers & Mathematics with Applications, 54 (1) (2007) 136-146.