Improving chemical problem-solving through the use of a fourteenth-order phase-fitting method

It is possible to eliminate phase-lag and all of its derivatives up to order five by employing a method that takes fading phase-lag into consideration. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new method called the cost-efficient approach. The unique method is illustrated by the symbol PF5DPHFITN142SPS. This approach is P-Stable, which means it is infinitely periodic. A wide variety of periodic and oscillatory issues can be solved using the suggested approach. The challenging problem of Schrödinger-type coupled differential equations in quantum chemistry was tackled using this novel approach. With only \(5\,FEvs\) $5FEvs$ needed to complete each step, the new method could be considered as a cost-effective approach. An AOR of 14 allows us to significantly improve our present condition.