In our present paper, we have obtained approximate solutions of non-linear quadratic Riccati differential equations using the Galerkin method. We considered Fibonacci polynomials and then Lucas polynomials as basis functions i.e., we presented two numerical methods: Fibonacci Galerkin method and Lucas Galerkin method. We have given some applications of this method by solving some differential equations. Then compare the approximate solution with the exact solution and approximate solutions with other methods. From this comparison and error analysis we can say that our method gives better results.
- Open Access
- Article
Solutions of Riccati Differential Equations by Galerkin Method Using Fibonacci and Lucas Polynomials
- Roji Bala *,†,
- Vinod Mishra †
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Received: 14 Oct 2025 | Revised: 11 Nov 2025 | Accepted: 09 May 2026 | Published: 25 May 2026
Abstract
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How to Cite
Bala, R.; Mishra, V. Solutions of Riccati Differential Equations by Galerkin Method Using Fibonacci and Lucas Polynomials. Nonlinear Analysis and Computer Simulations 2026, 1 (2), 9. https://doi.org/10.53941/nacs.2026.100009.
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