Category: Differential equations

A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems, M.M. Tung, E. Defez, J. Ibáñez, J.M. Alonso, J.I. Real-Herráiz, Mathematics 2022, 10(16), 2826, https://www.doi.org/10.3390/math10162826

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.

On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem, E. Defez, J. Ibáñez, J.M. Alonso, M.M. Tung, T.P. Real-Herraiz, Teresa Pilar. Mathematics, 2021, 9(18), 2262, https://doi.org/10.3390/math9182262

Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of special nonlinear third-order matrix differential equations, having the form 𝑌(3)(𝑥)=𝑓(𝑥,𝑌(𝑥)). Some numerical test problems are also included, whose solutions are computed by our method.