Premium
Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains
Author(s) -
Shivanian Elyas,
Jafarabadi Ahmad
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22126
Subject(s) - mathematics , radial basis function , basis function , nonlinear system , interpolation (computer graphics) , mathematical analysis , collocation (remote sensing) , thin plate spline , convergence (economics) , spectral method , stability (learning theory) , fractional calculus , spline interpolation , frame (networking) , bilinear interpolation , physics , remote sensing , quantum mechanics , machine learning , economic growth , artificial neural network , computer science , economics , telecommunications , statistics , geology
In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable inL 2and also convergent by the order of convergence O ( δ t 2 − α ) , 0 < α < 1 . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017