A Family of High Algebraic Order Embedded Explicit Six-Step Methods with Vanished Phase-Lag and its Derivatives for the Numerical Solution of the Schrodinger Equation and Related Problems

摘要

A family of eighth algebraic order embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of second order periodic initial or boundary-value problems is studied in this paper. The development of the new family of embedded methods is based on: ? the vanishing phase-lag and ? the vanishing of its derivatives. For the obtained methods of the new family of embedded methods, we studied their local truncation error and we calculate its asymptotic form after its application to a test problem which is equivalent with the radial Schrodinger equation. A comparison of the asymptotic forms of the resulting (after application to the test problem) formulae of the local truncation errors are compared in order to lead to summaries about the efficiency of each method of the family. We also investigated the stability and the interval of periodicity of the obtained methods of the new family of embedded methods. Finally, we applied the new produced family of embedded methods to the numerical solution of the radial Schrodinger equation in order to show their efficiency.