SPATIAL MANIFESTATIONS OF ORDER REDUCTION IN RUNGE-KUTTA METHODS FOR INITIAL BOUNDARY VALUE PROBLEMS

被引：0

作者：

Rosales, Rodolfo Ruben ^{[1
]}

Seibold, Benjamin ^{[2
]}

Shirokoff, David ^{[3
]}

Zhou, Dong ^{[4
]}

机构：

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Temple Univ, Dept Math, 1805 North Broad St, Philadelphia, PA 19122 USA

[3] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

[4] Calif State Univ, Dept Math, 5151 State Univ Dr, Los Angeles, CA 90032 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2024年 / 22卷 / 03期

基金：

美国国家科学基金会;

关键词：

Runge-Kutta; order reduction; boundary layer; stage order; weak stage order; modified boundary conditions; PARTIAL-DIFFERENTIAL-EQUATIONS; DEFERRED CORRECTION METHODS; GENERAL LINEAR METHODS; TIME DISCRETIZATIONS; FRACTIONAL ORDERS; STEP METHODS; CONVERGENCE; INTEGRATION; STABILITY; ACCURACY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the spatial manifestations of order reduction that occur when timeIBVPs, geometric structures arise that do not have an analog in ODE IVPs: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. To understand those boundary layers, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers persist over many time steps. Based on this, two remedies to order reduction are studied: first, a new condition on the Butcher tableau, called weak stage order, that is compatible with diagonally implicit Runge-Kutta schemes; and second, the impact of modified boundary conditions on the boundary layer theory is analyzed.

引用

页码：613 / 653

页数：41

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