Turkish Journal of Mathematics
Abstract
In this study, the Fubini collocation method is proposed for the approximate solution of nonlinear differential equations. The method utilizes fundamental relations involving Fubini polynomials and their derivatives, employing collocation points to enhance solution accuracy. Within this framework, the given differential equation is transformed into a system of nonlinear algebraic equations involving the unknown coefficients of the approximate solution. This resulting system is then solved using appropriate numerical techniques to obtain the approximate solution. The effectiveness of the proposed method is demonstrated through several test problems, with accuracy evaluated using absolute error functions. Furthermore, illustrative examples and residual-based error analysis confirm the method’s reliability.
DOI
10.55730/1300-0098.3640
Keywords
Fubini polynomials, nonlinear differential equation, collocation points, residual error analysis
First Page
138
Last Page
152
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
ERDEM BİÇER, K, & TÜRKHAN, H (2026). Fubini collocation method for numerical solutions of differential equations with quadratic and cubic nonlinearities. Turkish Journal of Mathematics 50 (1): 138-152. https://doi.org/10.55730/1300-0098.3640
