Sequential second derivative general linear methods for stiff systems. (English) Zbl 1302.65163
Summary: Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge-Kutta stability conditions. In this paper, we introduce a technique for construction of an special case of SGLMs which decreases the complexity of finding coefficients matrices.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L04 | Numerical methods for stiff equations |
