Fernández Fernández, Francisco JavierFernández Tojo, Fernando Adrián2020-11-102020-11-102020Fernández, F.J.; Tojo, F.A.F. Numerical Solution of Stieltjes Differential Equations. Mathematics 2020, 8, 1571http://hdl.handle.net/10347/23637This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue–Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based on Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence, and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation and use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based on a Stieltjes differential equation and a system of Stieltjes differential equations with several derivatorseng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Stieltjes ordinary differential equationLebesgue–Stieltjes quadrature formulaePredictor-corrector methodjournal article10.3390/math80915712227-7390open access