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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2019 / Cilt: 9 - Sayı: 2

A mixed method approach to Schrödinger equation: Finite difference method and quartic B-spline based differential quadrature method

Ali BAŞHAN
Pages
223–235
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The comparisonhas clearly indicated that the presently used method, namely FDM-DQM, isan appropriate and accurate numerical scheme and allowed us to present forsolving a wide class of partial differential equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The present manuscript includes finite difference method and quartic B-splinebased differential quadrature method (FDM-DQM) for getting the numericalsolutions for the nonlinear Schrödinger (NLS) equation.
📊
Key Findings & Data:To solve complex NLSequation firstly we have separated NLS equation into the two real value partialdifferential equations.
💡
Conclusion & Impact:The comparisonhas clearly indicated that the presently used method, namely FDM-DQM, isan appropriate and accurate numerical scheme and allowed us to present forsolving a wide class of partial differential equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The present manuscript includes finite difference method and quartic B-splinebased differential quadrature method (FDM-DQM) for getting the numericalsolutions for the nonlinear Schrödinger (NLS) equation. To solve complex NLSequation firstly we have separated NLS equation into the two real value partialdifferential equations. After that they are discretized in time using special typeof classical finite difference method namely, Crank-Nicolson scheme. Then, forspace integration differential quadrature method has been implemented. So,partial differential equation turn into simple a system of algebraic equations.To display the accuracy of the present hybrid method, the error norms L 2and L ∞ and two lowest invariants I 1 and I 2 and relative changes of invariantshave been calculated. As a last step, the numerical result already obtained havebeen compared with earlier studies by using same parameters. The comparisonhas clearly indicated that the presently used method, namely FDM-DQM, isan appropriate and accurate numerical scheme and allowed us to present forsolving a wide class of partial differential equations.

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Cite This Article

BAŞHAN, A. (2022). A mixed method approach to Schrödinger equation: Finite difference method and quartic B-spline based differential quadrature method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 9 - Sayı: 2, 223–235. https://ajindex.com/articles/440617

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