A reliable algorithm for solving higher order schrödinger equations with enhanced convergence

Abstract

This study introduces an efficient algorithm to solve higher-order Schrödinger equations using the power series method combined with Adomian polynomials in terms of solution coefficients. The explicit solution is derived through a first-order recurrence relation. To improve the convergence region, the Padé approximation is applied. The paper includes a detailed analysis of convergence, error control, and solution uniqueness, demonstrating the method's accuracy within a specified domain. Several illustrative examples are also presented to demonstrate the effectiveness and simplicity of the present method.