An integral formulation for the global error of Lie Trotter splitting scheme

ISSN: 2146-0957
Yayın Aralığı: Yılda 2 Sayı
Yayıncı: Prof. Dr. Ramazan YAMAN

An ordinary differential equation (ODE) can be split into simpler sub equationsand each of the sub equations is solved subsequently by a numerical method.Such a procedure involves splitting error and numerical error caused by thetime stepping methods applied to sub equations. The aim of the paper isto present an integral formula for the global error expansion of a splittingprocedure combined with any numerical ODE solver.

PDF

___

Hairer, E., Lubich, C. and Wanner, G. (2002). Geometric numerical integration: structure- preserving algorithms for ordinary differential equations. Springer.
Viswanath, D. (2001). Global errors of numer- ical ODE solvers and Lyapunov’s theory of stability. IMA Journal of Numerical Analysis, 21, 387-486.
Iserles, A. (2002). On the global error of dis- cretization methods for highly-oscillatory or- dinary differential equations. BIT Numerical Mathematics, 42, 561-599.
Sanz-Serna, J. M. and Calvo, P. (1994). Nu- merical Hamiltonian problems. Chapman & Hall.
Jahnke, T. and Lubich, C. (2000). Error bounds for exponential operator splittings. BIT Numerical Mathematics, 40, 735-744.
Hansen, E. and Ostermann, A. (2009). Ex- ponential splitting for unbounded operators. Mathematics of Computation, 78, 1485-1496.
Csomós, P. and Faragó, I. (2008). Error anal- ysis of the numerical solution of split differen- tial equations. Mathematical and Computer Modelling, 48, 1090-1106.
Ascher, U.M., Mattheij, R.M.M. and Russell, R.D. (1995). Numerical solution of bound- ary value problems for ordinary differential equations. Society for Industrial and Applied Mathematics.