| Abstract: |
| Runge-Kutta (RK) methods may demonstrate order reduction when applied to stiff problems. This talk explores the issue of order reduction in Runge-Kutta methods specifically when dealing with linear and semi-linear stiff problems. First, I will introduce Diagonally Implicit Runge-Kutta (DIRK) methods with high Weak Stage Order (WSO), capable of mitigating order reduction in linear problems with time-independent operators. On the theoretical front, I will present order barriers relating the WSO of an RK scheme to its order and the number of stages for fully-implicit RK and DIRKmethods, serving as a foundation to construct schemes with high WSO. I will conclude by presenting stiff order conditions for semilinear problems, essential to extend beyond the limitations of WSO, which primarily focused on linear problems. |
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