A very efficient and sophisticated fourteenth-order phase-fitting method for addressing chemical issues.

Applying a method with vanished phase–lag might potentially eliminate the phase–lag and its first, second, and third derivatives. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new strategy called the cost–efficient approach. Equation PF3DPHFITN142SPS demonstrates the unique method. The suggested approach is P–Stable, meaning it is indefinitely periodic. The suggested approach 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. [ABSTRACT FROM AUTHOR]