John C. Butcher is known primarily for his work in the field of numerical analysis, particularly in the area of numerical methods for solving ordinary differential equations (ODEs) and partial differential equations (PDEs). He is well-regarded for his development of various numerical integration methods, notably those related to Runge-Kutta methods. He has published many research papers and has contributed to the field through his academic work, which includes teaching and mentoring students in mathematics and numerical analysis.
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John C. Butcher works on numerical methods for ordinary differential equations, particularly Runge-Kutta methods and general linear methods. His research connects the algebraic structure of a numerical method with its approximation and numerical stability properties. The Butcher tableau records the stages and weights of a Runge-Kutta method compactly.[ref]
https://www.math.auckland.ac.nz/~butcher/biography.html. University of Auckland biography, Research Interests and 1991 mathematical-research award citation