1986/01/01 by L. F. Shampine · 172 citations
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #Numerical methods for differential equations #Electromagnetic Scattering and Analysis #Mathematics #Runge–Kutta methods #Interpolation (computer graphics) #Selection (genetic algorithm) #Applied mathematics #Calculus (dental) #Order (exchange) #Mathematical optimization #Mathematical analysis #Differential equation #Computer science #Artificial intelligence
paper · pdf · doi:10.2307/2008219
published in Mathematics of Computation 46(173), 135 (American Mathematical Society)
openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently regarded as "best".