Abstract
The aim of this paper is to investigate the accuracy and
efficiency of Gauss-type nested implicit Runge–Kutta (NIRK) methods.
These methods possess many important practical properties of implicit
Runge–Kutta (IRK) methods, such as, good stability, high order, and
symmetry. Moreover, as with IRK methods, NIRK methods can also be
presented in embedded form that helps local error estimation. However,
the implementation of NIRK methods is practically cheaper than other
classes of IRK methods as the NIRK formulas have explicit internal
stages.
We test an order six NIRK method that uses an embedded order four
method for estimating the local error. Our test problems are those from
stiff DETEST. As part of the testing, we compare the method with the
Matlab integrator ODE15s and assess the effectiveness of four variations
on the local error estimation
Attique Ur-Rehman, Shafiq Ur Rehman, Junaid Ahmad. (2019) Numerical Approximation of Stiff Problems Using Efficient Nested Implicit Runge–Kutta Methods, Punjab University Journal of Mathematics, Volume 51, Issue 2.
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