TY - JOUR
T1 - Numerical study of generalized 2-D nonlinear Schrödinger equation using Kansa method
AU - Pathak, Maheshwar
AU - Joshi, Pratibha
AU - Nisar, Kottakkaran Sooppy
N1 - Publisher Copyright:
© 2022 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2022/10
Y1 - 2022/10
N2 - The present study is influenced by the wide applications of the Schrödinger equations. Its occurrence can be easily seen in electromagnetic wave propagation, quantum mechanics, plasma physics, nonlinear optics, underwater acoustics, etc. Solving equations of this type is always difficult. In the current paper, we have discussed a very easy numerical technique which is also known as the Kansa method along with polyharmonic radial basis function for the numerical study of generalized 2-D nonlinear Schrödinger equations. The stability analysis of the present method is discussed. The efficiency and accuracy of the present method are demonstrated by considering three numerical cases along with different types of boundary conditions.
AB - The present study is influenced by the wide applications of the Schrödinger equations. Its occurrence can be easily seen in electromagnetic wave propagation, quantum mechanics, plasma physics, nonlinear optics, underwater acoustics, etc. Solving equations of this type is always difficult. In the current paper, we have discussed a very easy numerical technique which is also known as the Kansa method along with polyharmonic radial basis function for the numerical study of generalized 2-D nonlinear Schrödinger equations. The stability analysis of the present method is discussed. The efficiency and accuracy of the present method are demonstrated by considering three numerical cases along with different types of boundary conditions.
KW - Kansa method
KW - Nonlinear equation
KW - Partial differential equation
KW - Radial basis function
KW - Schrödinger equation
UR - https://www.scopus.com/pages/publications/85129472758
U2 - 10.1016/j.matcom.2022.04.030
DO - 10.1016/j.matcom.2022.04.030
M3 - Article
AN - SCOPUS:85129472758
SN - 0378-4754
VL - 200
SP - 186
EP - 198
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -