Cubic-matrix splines and second-order matrix models
arXiv:0711.29134 citationsh-index: 18
Originality Synthesis-oriented
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This work offers a new numerical approach for solving matrix differential equations, but it is incremental as it applies existing spline techniques to a specific problem class.
The paper proposes using cubic-matrix splines to approximate solutions of second-order matrix differential equations, providing an algorithm and error estimation. Numerical results demonstrate the method's effectiveness.
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.