Tính ổn định của phương pháp irk bước đôi một trên cơ sở các điểm sắp đặt theo thứ tự gauss-legendre và ứng dụng của nó

• Tác giả: Huu Cong Nguyen, Thu Thuy Nguyen
• Ngôn ngữ: vie
• Ký hiệu phân loại: 519.6 Mathematical optimization formerly 519.3
• Thông tin xuất bản: Vietnam Journal of Mathematics, 2012
• Mô tả vật lý: 115-126
• Bộ sưu tập: Metadata
• ID: 626467

Tóm tắt

This paper investigates a class of IRK-type methods for solving first-order stiff initial-value problems (IVPs). The IRK-type methods are constructed by using coefficients of s-stage collocation Gauss-Legendre IRK methods and other 2s-stage collocation IRK methods. The collocation points used in the 2s-stage methods are chosen such that at nth integration step, their stage values can be used as the stage values of the associated collocation Gauss-Legendre IRK methods for (n + 2)th integration step. By this way we obtain the methods in which the integration processes can be proceeded two-step-by-two-step. The resulting IRK-type methods are called two-step-by-two-step IRK methods based on Gauss-Legendre collocation points (TBTIRKG methods). Stability considerations show that these TBTIRKG methods can be A-stable or A(a)stable which can be applied to stiff IVPs with a fewer number of implicit relations that are to be solved in the integration process when compared with the traditional Gauss-Legendre IRK methods. The stability investigation results for TBTIRKG methods were applied in considerations of the asymptotic stability of a class of PC methdds based on the TBTIRKG methods.