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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A modified Butcher formula for integration of stiff systems of ordinary differential equations


Author: H. Nosrati
Journal: Math. Comp. 27 (1973), 267-272
MSC: Primary 65L05
MathSciNet review: 0329265
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Abstract: An A-stable one-step integration formula, called the modified Butcher (MB), is presented and is shown to have an order of accuracy $ p = 3$, when the differential system is linear, and $ p = 2$ otherwise. A method for evaluating the local truncation error of the formula is also suggested. Finally, the main features of this formula, vis-a-vis the trapezoidal, are compared.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0329265-3
PII: S 0025-5718(1973)0329265-3
Keywords: Stiff system of ordinary differential equations, A-stability, Newton-Raphson iterations, Butcher's implicit Runge-Kutta process
Article copyright: © Copyright 1973 American Mathematical Society