6533b872fe1ef96bd12d41f5

RESEARCH PRODUCT

Magnus and Fer expansions for matrix differential equations: the convergence problem

J A OteoFernando CasasJosé Luis Regidor RosSergio Blanes

subject

State-transition matrixMatrix differential equationMathematical analysisGeneral Physics and AstronomyStatistical and Nonlinear PhysicsGeneral MedicineMatrix (mathematics)Linear differential equationMagnus expansionDifferential algebraic equationUniversal differential equationMathematical PhysicsMathematicsStiffness matrix

description

Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.

yearjournalcountryeditionlanguage
1998-01-09Journal of Physics A: Mathematical and General
https://doi.org/10.1088/0305-4470/31/1/023