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arXiv · 2409.20369

Numerical solutions of ordinary differential equations using Spline-Integral Operator

Gustavo H. O. Salgado·João P. R. Romanelli
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Abstract

In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order.

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Gustavo H. O. Salgado, João P. R. Romanelli. 2024-09-30. Numerical solutions of ordinary differential equations using Spline-Integral Operator. https://arxiv.org/abs/2409.20369

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