Two Optimized Symmetric Eight-Step Implicit Methods for Initial-Value Problems with Oscillating Solutions

Details Two Optimized Symmetric Eight-Step Implicit Methods for Initial-Value Problems with Oscillating Solutions Two Optimized Symmetric Eight-Step Implicit Methods for Initial-Value Problems with Oscillating Solutions

2008-11-15

arxiv.org/abs/0811.2470v1

Mathematics

Numerical Analysis

20 pages, 7 figures

Scientific paper

In this paper we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schr\"odinger equation with the use of the Woods-Saxon potential. They can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the two new methods to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved.

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