Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schr ö dinger Equation with Energy and Mass Conversion

Xuan Liu, Muhammad Ahsan, Masood Ahmad, Muhammad Nisar, Xiaoling Liu, Imtiaz Ahmad and Hijaz Ahmad
Additional contact information
Xuan Liu: Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China
Muhammad Ahsan: Department of Mathematics, University of Swabi, Swabi 23200, Pakistan
Masood Ahmad: Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan
Muhammad Nisar: Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia
Xiaoling Liu: Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China
Imtiaz Ahmad: Department of Mathematics, University of Swabi, Swabi 23200, Pakistan
Hijaz Ahmad: Department of Computer Engineering, Biruni University, Istanbul 34025, Turkey

Energies, 2021, vol. 14, issue 23, 1-17

Abstract: This article is concerned with the numerical solution of nonlinear hyperbolic Schr o ¨ dinger equations (NHSEs) via an efficient Haar wavelet collocation method (HWCM). The time derivative is approximated in the governing equations by the central difference scheme, while the space derivatives are replaced by finite Haar series, which transform it to full algebraic form. The experimental rate of convergence follows the theoretical statements of convergence and the conservation laws of energy and mass are also presented, which strengthens the proposed method to be convergent and conservative. The Haar wavelets based on numerical results for solitary wave shape of | φ | are discussed in detail. The proposed approach provides a fast convergent approximation to the NHSEs. The reliability and efficiency of the method are illustrated by computing the maximum error norm and the experimental rate of convergence for different problems. Comparisons are performed with various existing methods in recent literature and better performance of the proposed method is shown in various tables and figures.

Keywords: conservative scheme; Haar wavelet; collocation method; Schr ö dinger equation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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