On the solution of high order stable time integration methods

Boundary value problems

Stanislav Sysala¹  Bashir Ahmad¹  Radim Blaheta¹  Owe Axelsson² 

[1] IT4 Innovations Department, Institute of Geonics AS CR, Ostrava, Czech Republic;King Abdulaziz University, Jeddah, Saudi Arabia

关键词: Parabolic Problem;    Discretization Error;    Quadrature Point;    Finite Difference Approximation;    Implicit Euler Method;   

DOI  :  10.1186/1687-2770-2013-108

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Evolution equations arise in many important practical problems. They are frequently stiff, i.e. involves fast, mostly exponentially, decreasing and/or oscillating components. To handle such problems, one must use proper forms of implicit numerical time-integration methods. In this paper, we consider two methods of high order of accuracy, one for parabolic problems and the other for hyperbolic type of problems. For parabolic problems, it is shown how the solution rapidly approaches the stationary solution. It is also shown how the arising quadratic polynomial algebraic systems can be solved efficiently by iteration and use of a proper preconditioner.

【 授权许可】

CC BY