A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrodinger equation and related orbital problems

作者：Panopoulos G A; Simos T E^*

来源：Journal of Mathematical Chemistry, 2013, 51(7): 1914-1937.

DOI：10.1007/s10910-013-0184-1

• Schrodinger equation
• SEPCM
• Orbital problems
• Phase-lag
• Initial value problems
• Oscillatory solution
• Symmetric
• Multistep
• Eight-step
• Second-order IVPs
• Predictor-corrector

In this work we introduce a new predictor-corrector (PC) pair form (SEPCM) for the numerical integration of second-order initial-value problems and a new optimized eight-step symmetric predictor-corrector method with minimal phase-lag and algebraic order ten is constructed. The new method is based on the multistep symmetric method of Quinlan-Tremaine (Astron. J. 100(5):1694-1700, 1990), with eight steps and eighth algebraic order and constructed to solve numerically the radial time-independent Schrodinger equation during the resonance problem with the use of the Woods-Saxon potential. It can also be used to integrate related IVPs with oscillatory solutions such as orbital problems. We compare the new method to some recently constructed optimized methods and other methods from the literature. We measure the efficiency of the methods and conclude that the new optimized method is the most efficient of all the compared methods and for all the problems solved.

• 出版日期2013-8