Multi-adaptive Galerkin methods for ODEs V: Stiff problems

نویسندگان

  • Johan Jansson
  • Anders Logg
چکیده

We develop the methodology of multi-adaptive time-stepping for stiff problems. The new algorithm is based on adaptively stabilized fixed point iteration on time slabs and a new method for the recursive construction of time slabs. Numerical examples are given for a series of well-known stiff and non-stiff test problems.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize

Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...

متن کامل

Multi-Adaptive Galerkin Methods for ODEs II: implementation and Applications

Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879–1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete equations, features of the implementation Tanganyika, and computational results for a variety of ODEs. Examples include the Lorenz system, th...

متن کامل

Multi-Adaptive Galerkin Methods for ODEs I

We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual timesteps, order and quadrature, so that in particular each individual component has its own time-step sequence. This paper contains a description of the methods, an analysis of their basic properties, and a posteriori error analy...

متن کامل

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes

Despite the popularity of high-order explicit Runge–Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit–explicit Runge–Kutta (IMEX-RK) schemes to overcome geometry...

متن کامل

Adaptive Linear Equation Solvers in Codes for Large Stiff Systems of ODEs

Iterative linear equation solvers have been shown to be effective in codes for large systems of stiff initial-value problems for ordinary differential equations (ODEs). While preconditioned iterative methods are required in general for efficiency and robustness, unpreconditioned methods may be cheaper over some ranges of the interval of integration. In this paper, we develop a strategy for swit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004