Abstract
Gauss-type nested implicit Runge–Kutta methods exhibit many
vital properties of implicit Runge–Kutta methods, such as stability, highorder accuracy, and symmetry. Moreover, nested implicit Runge–Kutta
methods have a cheap practical implementation in comparison of implicit
Runge–Kutta methods because of their explicit nature of internal stages.
In this paper, we provide a complete mechanism for the construction,
formulation, and implementation of 4
th- and 6
th-order nested implicit
Runge–Kutta methods. The numerical testing is performed using 6
th
-
order nested implicit Runge–Kutta method that uses an embedded 4
th
-
order nested implicit Runge–Kutta method for the local error estimation
on a collection of test problems from stiff detest. We also compare the
nested implicit Runge–Kutta method with the MATLAB integrator ode15s
and assess the effectiveness of four variations on the local error estimation
Attique Ur-Rehman, Junaid Ahmad, Shafiq Ur Rehman. (2019) Efficient Nested Implicit Runge–Kutta Methods for Nonlinear Stiff Problems, Punjab University Journal of Mathematics, Volume 51, Issue 6.
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