In this article, we propose a numerical method based on alternative Legendre polynomials for approximating the solutions of two-dimensional linear and nonlinear Volterra-Fredholm integral equations. Alternative Legendre polynomials, known for their some special features and simplicity in constructing operational matrices, provide an efficient basis for this method. By employing the integration and product operational matrices of alternative Legendre polynomials, the integral equations are reduced to a system of algebraic equations, simplifying the computational process. Error analysis is conducted to assess the method’s accuracy, and several examples are presented to validate the high precision and efficiency of the proposed approach. The results confirm the accuracy and effectiveness of the method in solving complex integral equations.
Mohammadi, F. , Mirzaee, F. , Solhi, E. and Mahmoudi, S. (2025). A novel numerical approach for solving two-dimensional Volterra-Fredholm integral equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.65501.3016
MLA
Mohammadi, F. , , Mirzaee, F. , , Solhi, E. , and Mahmoudi, S. . "A novel numerical approach for solving two-dimensional Volterra-Fredholm integral equations", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.65501.3016
HARVARD
Mohammadi, F., Mirzaee, F., Solhi, E., Mahmoudi, S. (2025). 'A novel numerical approach for solving two-dimensional Volterra-Fredholm integral equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.65501.3016
CHICAGO
F. Mohammadi , F. Mirzaee , E. Solhi and S. Mahmoudi, "A novel numerical approach for solving two-dimensional Volterra-Fredholm integral equations," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.65501.3016
VANCOUVER
Mohammadi, F., Mirzaee, F., Solhi, E., Mahmoudi, S. A novel numerical approach for solving two-dimensional Volterra-Fredholm integral equations. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.65501.3016
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