Non-autonomous Riccati-type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds

Abstract

In this paper, non-autonomous Riccati-type matrix differential equations with twice continuously differentiable coefficients are considered. First of all an existence interval in terms of the data for an initial-value problem is determined. Secondly, a discrete numerical solution is constructed at a net of points of the predetermined existence interval using linear one-step matrix methods. Finally, using linear B -spline matrix functions, a continuous numerical solution with error bounds is obtained. Given an admissible error ε>0 we construct a continuous numerical solution whose error is uniformly upper bounded by ε in the existence domain.