Numerical computation of the coefficients in exponential fitting (Q2035512)

Two classes of Numerov methods based on exponential fitting are considered to solve the Schrödinger equation. The first class of methods is defined by methods depending on three parameters that includes the well-known methods \(S_m\), \(m=0,1,2,3\), characterized by known analytical expressions for the coefficients. These relations are established in the literature under a convenient condition: the maximum number of parameters that can be different is only two. The second class is defined by methods depending on five parameters. For general Numerov methods based on exponential fitting dependent on three or five parameters, linear systems are established for the coefficients and no closed formulas are known. This problem is solved in this paper using subroutines accessible in the literature. The analysis of the accuracy of the new methods is presented.