Abstract
In this paper we develop a more efficient three-stage implicit Runge-Kutta method of order 6 for solving first order initial value problems of ordinary differential equations. Collocation method is used to derive Continuous schemes in which both the interpolation and collocation points are at perturbed Gaussian points. This gives a higher order scheme, which is more efficient and stable than the existing similar ones. Simple linear problems are used to check its level of accuracy and stability. Key words: Implicit, more efficient, stable, collocation methods, Perturbed Gaussian points and error estimates.
Highlights
Implicit Runge-Kutta methods are A-stable and very efficient for solving both Stiff and non- Stiff problems of ordinary differential equations (ODEs)
Implicit RungeKutta methods were earlier developed by Kuntzmann (Butcher, 1964, 1988) etc
The construction of multiply or full implicit methods are based on the theory of Gauss quadrature, where the nodes of integration are the transformed zeros of Legendre polynomial from (-1, 1) onto (0,1)
Summary
A highly efficient implicit Runge-Kutta method for first order ordinary differential equations. In this paper we develop a more efficient three-stage implicit Runge-Kutta method of order 6 for solving first order initial value problems of ordinary differential equations. Continuous schemes in which both the interpolation and collocation points are at perturbed Gaussian points. This gives a higher order scheme, which is more efficient and stable than the existing similar ones. Simple linear problems are used to check its level of accuracy and stability
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