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Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treatmultiscale equations that contain a stiff part and a non-stiff part, where thestiff part is characterized by a small parameter $\varepsilon$. In this work,we prove rigorously the uniform stability and uniform accuracy of a class ofIMEX-RK schemes for a linear hyperbolic system with stiff relaxation. Theresult we obtain is optimal in the sense that it holds regardless of the valueof $\varepsilon$ and the order of accuracy is the same as the design order ofthe original scheme, i.e., there is no order reduction.

Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation