Numerical solutions of ordinary differential equations using Spline-Integral Operator
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...
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| Veröffentlicht in: | arXiv.org 2024-09 |
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| creator | Salgado, Gustavo H O Romanelli, João P R |
| description | 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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| language | eng |
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| subjects | Boundary value problems Differential equations Exact solutions Mathematical analysis Numerical methods Operators (mathematics) Stability analysis |
| title | Numerical solutions of ordinary differential equations using Spline-Integral Operator |
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