Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Journal of Computational and Applied Mathematics
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Two trigonometrically fitted methods based on a classical Runge-Kutta method of Kutta-Nystrom are being constructed. The new methods maintain the fifth algebraic order of the classical one but also have some other significant properties. The most important one is that in the local truncation error of the new methods the powers of the energy are lower and that keeps the error at lower values, especially at high values of energy. The error analysis justifies the actual results when integrating the radial Schrodinger equation, where the high efficiency of the new methods is shown.