The use of a multistep, cost-efficient fourteenth-order phase-fitting method to chemistry problems

Applying a phase-fitting method might potentially vanish the phase-lag and its first derivative. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new strategy called the cost-efficient approach. Equation PF1DPHFITN142SPS demonstrates the unique method. The suggested approach is P-Stable, meaning it is indefinitely periodic. The proposed method is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5FEvs to run each stage, it may be considered a cost-efficient approach. With an AOR of 14, we can significantly improve our present predicament.