A low-cost, two-step fourteenth-order phase-fitting approach to tackling problems in chemistry.

The phase-lag and all of its derivatives (first, second, third, fourth, fifth, and sixth) might be eliminated using a phase-fitting technique. The new approach, which is referred to as the economical method, targets maximizing algebraic order (AOR) and reducing function evaluations (FEvs). The one-of-a-kind approach is demonstrated by Equation PF6DPFN142SPS.The proposed method is infinitely periodic i.e. P-Stable. To many periodic and/or oscillatory problems, the suggested strategy can be applied. Using this innovative method, the difficult issue of Schrödinger-type coupled differential equations was tackled in quantum chemistry. Every step of the new approach only requires 5FEvs to execute, making it a economic algorithm. By accomplishing a AOR of 14, this allows us to greatly enhance our current situation. [ABSTRACT FROM AUTHOR]