Two FORTRAN packages for assessing initial value methods
ACM Transactions on Mathematical Software (TOMS)
Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
ACM Transactions on Mathematical Software (TOMS)
A family of fifth-order Runge-Kutta pairs
Mathematics of Computation
A general family of explicit Runge-Kutta pairs of orders 6(5)
SIAM Journal on Numerical Analysis
Cheap Error Estimation for Runge--Kutta Methods
SIAM Journal on Scientific Computing
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Dynamic modeling and control of an octopus inspired multiple continuum arm robot
Computers & Mathematics with Applications
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Among the most popular methods for the solution of the Initial Value Problem are the Runge-Kutta pairs of orders 5 and 4. These methods can be derived solving a system of nonlinear equations for its coefficients. To achieve this, we usually admit various simplifying assumptions. The most common of them are the so-called row simplifying assumptions. Here we neglect them and present an algorithm for the construction of Runge-Kutta pairs of orders 5 and 4 based only in the first column simplifying assumption. The result is a pair that outperforms other known pairs in the bibliography when tested to the standard set of problems of DETEST. A cost free fourth order formula is also derived for handling dense output.