Cubic-matrix splines and second-order matrix models

TL;DR

This paper explores the application of cubic-matrix splines to approximate solutions of second-order matrix differential equations, providing error estimates, algorithms, and an illustrative example.

Contribution

It introduces a novel approach using cubic-matrix splines for solving matrix models of the form Y''(x) = f(x,Y(x)), including implementation details and error analysis.

Findings

Effective approximation of matrix models using cubic-matrix splines

Error estimation and algorithm for implementation provided

Numerical example demonstrating the method's applicability

Abstract

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.