Two-step Runge-Kutta Methods with Quadratic Stability Functions

被引：0
作者：
D. Conte
R. D’Ambrosio
Z. Jackiewicz
机构：
[1] Università di Salerno,Dipartimento di Matematica e Informatica
[2] Arizona State University,Department of Mathematics
[3] AGH University of Science and Technology,undefined
来源：
Journal of Scientific Computing | 2010年 / 44卷
关键词：
Two-step Runge-Kutta methods; Order conditions; Quadratic stability polynomials; Absolute stability; -stability; -stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions. We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.
引用
收藏
页码：191 / 218
页数：27
相关论文
共 40 条
[1]  
Bartoszewski Z.(1998)Construction of two-step Runge-Kutta methods of high order for ordinary differential equations Numer. Algorithms 18 51-70
[2]  
Jackiewicz Z.(2005)Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations Appl. Numer. Math. 53 149-163
[3]  
Bartoszewski Z.(2007)Derivation of continuous explicit two-step Runge-Kutta methods of order three J. Comput. Appl. Math. 205 764-776
[4]  
Jackiewicz Z.(1992)Local error estimation for singly-implicit formulas by two-step Runge-Kutta methods BIT 32 104-117
[5]  
Bartoszewski Z.(1978)A special family of Runge-Kutta methods for solving stiff differential equations BIT 18 22-41
[6]  
Jackiewicz Z.(1980)An implementation of singly implicit Runge-Kutta methods BIT 20 326-340
[7]  
Bellen A.(1979)A transformed implicit Runge-Kutta method J. Assoc. Comput. Mach. 26 731-738
[8]  
Jackiewicz Z.(1993)Diagonally-implicit multi-stage integration methods Appl. Numer. Math. 11 347-363
[9]  
Zennaro M.(1998)Construction of high order diagonally implicit multistage integration methods for ordinary differential equations Appl. Numer. Math. 27 1-12
[10]  
Burrage K.(1997)Order conditions for two-step Runge-Kutta methods Appl. Numer. Math. 24 351-364
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