Abstract
We generalize the RKrvQz algorithm to solve nonstiff initial-value problems in ordinary differential equations. The algorithm can now be applied to systems of nonstiff initial-value problems (IVPs) in ordinary differential equations, and both relative error and absolute error can be controlled, locally and globally. We demonstrate the algorithm by solving the simple harmonic oscillator for moderate and strict tolerances.
Highlights
We described the RKrvQz algorithm (Prentice, 2011) for solving nonstiff initial-value problems (IVPs) in ordinary differential equations (ODEs)
The algorithm can be applied to systems of nonstiff initial-value problems (IVPs) in ordinary differential equations, and both relative error and absolute error can be controlled, locally and globally
We demonstrate the algorithm by solving the simple harmonic oscillator for moderate and strict tolerances
Summary
We described the RKrvQz algorithm (Prentice, 2011) for solving nonstiff initial-value problems (IVPs) in ordinary differential equations (ODEs). This algorithm uses three explicit Runge-Kutta (RK) methods, of orders r, v and z, to control both local and global errors in a stepwise manner. We considered control of absolute error only, neglecting relative error control, and we considered the application of the algorithm to scalar problems, rather than systems of ODEs. The motivation for developing RKrvQz is that, in local extrapolation, the RKv solution is used to estimate the local error in the RKr solution, but the RKv solution is propagated in the RKr method. ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ , wi,n wherein the first index in the subscript indicates iteration number, and the second index indicates component
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