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- Title
Family of phase fitted 3-step second-order BDF methods for solving periodic and orbital quantum chemistry problems.
- Authors
Saadat, Hosein; Kiyadeh, Sanaz Hami Hassan; Karim, Ramin Goudarzi; Safaie, Ali
- Abstract
In this paper, we introduce a novel series of second-order Backward Differentiation Formulas (BDFs) specifically designed to address phase-lag and its first derivative in the numerical resolution of Initial Value Problems (IVPs) with orbital solutions. Our methodology commences with an in-depth analysis of phase-lag phenomena associated with second-order BDFs. Following this, we construct a suite of equations by embedding algebraic functions into the operational framework of the 3-step second-order BDF (SOBDF) method. Additionally, we elaborate on equations that precisely describe the phase-lag and its derivatives, with a concentrated focus on the 3-step SOBDF method. The culmination of this work is the presentation of six distinct methods, each methodically crafted to negate both the real and imaginary elements of phase-lag and its derivatives in numerical computations. The study advances with a meticulous examination of the local truncation error and the stability regions pertinent to the six phase-fitted methods introduced. Furthermore, we scrutinize their computational performance by deploying these methods across a spectrum of initial value problems, offering valuable insights into their effectiveness in varying contexts.
- Subjects
INITIAL value problems; QUANTUM chemistry; ALGEBRAIC equations; ALGEBRAIC functions
- Publication
Journal of Mathematical Chemistry, 2024, Vol 62, Issue 6, p1223
- ISSN
0259-9791
- Publication type
Article
- DOI
10.1007/s10910-024-01619-3