An Extended Picard Method to solve non-linear systems of ODE with applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915182363541504 |
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| author | Gadella, Manuel Lara, Luis P. |
| author_facet | Gadella, Manuel Lara, Luis P. |
| contents | We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This method is a mixture between an iterative process, a la Picard, plus a segmentary integration, which gives explicit approximate solutions in terms of trigonometric functions and polynomials. The segmentary part is particularly important if the integration interval is large. This procedure provide a new tool so as to obtain approximate solutions of systems of interest in the analysis of chemical reactions. We test the method on some classical equations like Mathieu, Duffing quintic equation or Bratu's equation and have applied it on some models of chemical reactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Extended Picard Method to solve non-linear systems of ODE with applications Gadella, Manuel Lara, Luis P. Classical Analysis and ODEs 34A99 We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This method is a mixture between an iterative process, a la Picard, plus a segmentary integration, which gives explicit approximate solutions in terms of trigonometric functions and polynomials. The segmentary part is particularly important if the integration interval is large. This procedure provide a new tool so as to obtain approximate solutions of systems of interest in the analysis of chemical reactions. We test the method on some classical equations like Mathieu, Duffing quintic equation or Bratu's equation and have applied it on some models of chemical reactions. |
| title | An Extended Picard Method to solve non-linear systems of ODE with applications |
| topic | Classical Analysis and ODEs 34A99 |
| url | https://arxiv.org/abs/2503.02856 |