Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12

• 作者: Huong Nguyen-Thu Re′mi Vaillancourt Truong Nguyen-Ba
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Strong Stability PRESERVING Hermite-Birkhoff Method SSP Coefficient TIME Discretization Method of Lines Comparison with Other SSP Methods
• 年，卷（期）: 2011,（2）
• 页码范围: 72-82
• 页数: 11页
• 分类号: O1

摘要

We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.