@article { author = {Sadek, Lakhlifa and Talibi Alaoui, Hamad}, title = {The extended block Arnoldi method for solving generalized differential Sylvester equations}, journal = {Journal of Mathematical Modeling}, volume = {8}, number = {2}, pages = {189-206}, year = {2020}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2020.15871.1388}, abstract = {In the present paper, we propose a new method for solving large-scale generalized differential Sylvester equations, by projecting the initial problem onto the extended block Krylov subspace with an orthogonality Galerkin condition. This projection gives rise to a low-dimensional generalized differential Sylvester matrix equation. The low-dimensional equations is then solved by Rosenbrock or BDF method. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.}, keywords = {Extended block Krylov subspace,Generalized differential Sylvester matrix equation,low-rank approximate solution,Rosenbrock method,BDF method}, url = {https://jmm.guilan.ac.ir/article_3969.html}, eprint = {https://jmm.guilan.ac.ir/article_3969_444c1efce1282718615df9f44418d764.pdf} }