Numerical Solution of Stieltjes Differential Equations

Francisco J. Fernández and F. Adrián F. Tojo
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Francisco J. Fernández: Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
F. Adrián F. Tojo: Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain

Mathematics, 2020, vol. 8, issue 9, 1-30

Abstract: This 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 derivators.

Keywords: Stieltjes ordinary differential equation; Lebesgue–Stieltjes quadrature formulae; predictor-corrector method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:9:p:1571-:d:412423

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