In this paper Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve nonlinear partial differential equations (PDEs) in right triangles. These algorithms evaluate more times the function than a standard explicit Runge–Kutta scheme (n_t times per step), and these extra evaluations do not increase the order of convergence but the stability region grows with O(nt2). Hence, the total computational cost is O(nt) times lower than with a traditional explicit algorithm. Thus, these algorithms have been traditionally considered to solve stiff PDEs in squares/rectangles or cubes. In this paper, for the first time, ESERK methods are considered in a right triangle. It is demonstrated that such type of codes keep the convergence and the stability properties under certain conditions. This new approach would allow to solve nonlinear parabolic PDEs with stabilized explicit Runge–Kutta schemes in complex domains, that would be decomposed in rectangles and right triangles.

本文提出外推稳定显式Runge-Kutta方法（ESERK）来求解直角三角形中的非线性偏微分方程（PDE）。与标准的显式Runge-Kutta方案（ñ_Ť 每步次），并且这些额外的评估不会增加收敛的顺序，但是稳定区域会随着 Ø（ñŤ2）。因此，总的计算成本为Ø（ñŤ）比传统的显式算法低十倍。因此，传统上已考虑将这些算法用于求解正方形/矩形或立方体中的刚性PDE。本文首次在直角三角形中考虑了ESERK方法。证明了这种类型的代码在某些条件下保持收敛性和稳定性。这种新方法将允许在复杂域中使用稳定的显式Runge-Kutta方案求解非线性抛物线型PDE，这些非线性分解将分解为矩形和直角三角形。