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This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y(x)=f(x,Y(x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix differential equations are given.
We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type $Y(x) = f(x,Y(x))$. For numerical illustration, an estimation of the approximation error, an algorithm for its implementation, and an example are given.
The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly amount of
We consider differential Lyapunov and Riccati equations, and generalize
We consider the application of implicit and linearly implicit (Rosenbrock-type) peer methods to matrix-valued ordinary differential equations. In particular the differential Riccati equation (DRE) is investigated. For the Rosenbrock-type schemes, a r
We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the differenti