A new trigonometrically-fitted sixth algebraic order P-C algorithm for the numerical solution of the radial schrödinger equation

• Published in: Mathematical and computer modelling Vol. 42; no. 7; pp. 887 - 902
• Main Authors: Psihoyios, G., Simos, T.E.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2005; Elsevier Science
• Subjects: Exact sciences and technology; Exponential-fitting; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; P-C methods; Partial differential equations; Partial differential equations, boundary value problems; Schrödinger equation; Sciences and techniques of general use; Trigonometrical fitting; P-C methods; Trigonometrical fitting; Schrödinger equation; Exponential-fitting; Adams method; Predictor corrector method; PC method; Schrodinger equation; Radial equation; Efficiency; Applied mathematics; Numerical solution; Numerical algorithm
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2005.09.017

The new scheme developed in this paper is a new trigonometrically-fitted predictor-corrector (P-C) scheme based on the Adams-Bashforth-Moulton P-C methods. In particular, our predictor is based on the fifth algebraic order Adams-Bashforth scheme and our corrector on the sixth algebraic order Adams-Moulton scheme. We compared the efficiency of this new scheme against well known methods and the numerical experimentations showed that our scheme is more efficient, even when compared to methods that have been specially designed for the solution of the radial Schrödinger equation.