A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems

Abstract

Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our previous research results, to represent the solutions of nonlinear matrix differential problems of fourth order given in the form Y(4)(x)=f(x,Y(x)) in terms of higher-order matrix splines. The corresponding algorithm is explained, and some numerical examples for the illustration of the method are included.