Search

The phase lag and its first derivative can all vanish when utilising a phase-fitting strategy. Since the new method employs the highest possible algebraic order (AOR) while simultaneously requiring the fewest possible function evaluations (FEvs), it has been termed the economical method. A formula of PF1DPFN142SPS represents this novel approach. The P-Stable method is the one that is being proposed (i.e. infinitely periodic). Numerous issues with periodic and/or oscillating solutions can be addressed with the proposed method. We took this novel strategy to solve the difficult problem of Schrödinger—type coupled differential equations in quantum chemistry. The new tactic is known as a economic algorithm since it requires just 5FEvs at each stage to reach a 14AOR. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

A phase-fitting approach allows vanishing for not only the phase lag but also its first, second, third, fourth, fifth, and sixth derivatives to be considered. The new technique is dubbed economical method because it uses the maximum possible algebraic order (AOR) while simultaneously performing the fewest possible function evaluations (FEvs). The formula for this innovative method is PF6DPFN2SPS. The proposed technique is P-Stable (i.e. infinitely periodic). The proposed approach can be used to solve a variety of problems with periodic and/or oscillating solutions. To address the intractable nature of Schrödinger-type coupled differential equations in quantum chemistry, we adopted this unique approach. The new strategy is classified as a economic algorithm since it uses 5FEvs at each step to achieve a 12AOR. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

The phase lag and its first, second, third, fourth, and fifth derivatives are all accounted for in a phase-fitting method. The new system uses the fewest possible function evaluations per integration step (FEvs) to achieve the highest possible algebraic order (AOR) and is hence P-stable. PF5DPFN2SPS is the symbol for the new method. The proposed method can be used for many different problems with periodic and/or oscillating solutions. We used the unique approach to the well-known problem in quantum chemistry posed by Schrödinger-type coupled differential equations. The new method is part of the economic algorithms since it uses 5 FEvs at each stage to achieve a 12 AOR. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Methods for fitting the phase-lag and its first, second, third, and fourth derivatives are incorporated into a phase-fitting strategy. The novel system is singularly P-stable and is a member of the economic algorithm’s family (i.e., algorithms that employ the smallest number of function evaluations per integration step (FEvs) to obtain the largest algebraic order (AOR)). The notation for the new strategy is PF4DPFN2SPS. Numerous problems involving periodic and/or oscillating solutions can be resolved utilizing the proposed strategy. We applied the novel method to the coupled differential equations of Schrödinger type, a famous problem in quantum chemistry. The new technique utilizes 5 FEvs every step to reach a AOR of 12 and so belongs to the economic algorithms. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

This paper investigates the problem of computing the time-varying 2,3- and 2,4-inverses through the zeroing neural network (ZNN) method, which is presently regarded as a state-of-the-art method for computing the time-varying matrix Moore–Penrose inverse. As a result, two new ZNN models, dubbed ZNN23I and ZNN24I, for the computation of the time-varying 2,3- and 2,4-inverses, respectively, are introduced, and the effectiveness of these models is evaluated. Numerical experiments investigate and confirm the efficiency of the proposed ZNN models for computing the time-varying 2,3- and 2,4-inverses. © 2022 by the authors.

An approach to phase-fitting is devised, which includes methods for fitting the phase-lag and for fitting its first, second, and third derivatives. Singularly P-Stable, the novel system belongs to the family of economic algorithms [(i.e. algorithms which use the minimum number of function evaluations (FEvs) per integration step in order to achieve the maximum algebraic order (AOR)]. The new approach is denoted by the notation PF3DPFN2SPS. The proposed method can be used to solve a wide range of problems involving periodic and/or oscillating solutions. We applied the novel approach to a well-known problem in quantum chemistry, the Schrödinger-type coupled differential equations. To reach an AOR of 12, the new technique makes use of 5 FEvs per step and for this belongs to the economic algorithms. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

A phase-fitting, first and second derivatives phase-fitting method is produced. The new algorithm is singularly P-Stable and belongs to the economic algorithms. The new method is symbolized as PF2DPFN2SPS. It can be used to any problem with periodical and/or oscillating solutions. We chosen to be applied to a well known problem of Quantum Chemistry. The new scheme is an economic one because 5 function evaluations per step are used in order an algebraic order (AOR) of 12 to be achieved. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

A new two-step method, for the numerical solution of problems in quantum chemistry, is introduced in the present paper. The new algorithm is conditionally P-Stable and an economical scheme. It has vanished phase–lag and it’s first to fourth derivatives. We use for the new scheme the symbol LOWPF4DECN2ST. We apply the newly introduced method to problems in Quantum Chemistry. The new scheme is defined as economical since it uses 4 function evaluations per step in order to achieve an algebraic order (AOR) of 10. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.