An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues

In order to get rid of the phase-lag and its first, second, third, fourth, and fifth derivatives, a phase-fitting method might be applied. The new strategy, called the economical method, maximizes algebraic order (AOR) while minimizing function evaluations (FEvs). Equation PF5DPFN142SPS describes the unique method. An infinitely periodic P-Stable technique is suggested. The proposed method is applicable to numerous problems with periodic and/or oscillatory solutions. In quantum chemistry, this novel approach was used to address the challenging problem of Schrödinger-type coupled differential equations. It is an economic algorithm because each step of the new method only costs 5FEvs to carry out. This helps us to improve our existing condition significantly by achieving an AOR of 14.