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Computational methods and dynamical analysis for studying (1+1) dimensional functional equations of mixed integro-differential type

Gorde:
Argitaratua izan da:Boundary Value Problems vol. 2025, no. 1 (Dec 2025), p. 108
Egile nagusia: Mahdy, Amr M. S.
Beste egile batzuk: Abdou, Mohamed A., Mohamed, Doaa S.
Argitaratua:
Hindawi Limited
Gaiak:
Approximation
Error analysis
Polynomials
Difference equations
Linear algebra
Differential equations
Integral equations
Functional equations
Collocation methods
Sarrera elektronikoa:Citation/Abstract
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Laburpena:In the present paper, the Fibonacci collocation method is implemented to solve (1+1)<inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="13661_2025_2078_Article_IEq1.gif" /> dimensional difference equations of mixed integro-differential type. First, using the quadratic numerical technique, the mixed functional integro-differential equations are reduced to a system of Fredholm functional integro-differential equations in one dimension. Then, the Fibonacci collocation method is applied to transform the Fredholm functional integro-differential equations into a system of linear algebraic equations. The convergence analysis of the functional integro-differential equations is discussed. The method’s error analysis is presented. Several examples are provided to demonstrate the use of the Fibonacci collocation approach. Maple 18 is used to carry out all of the numerical calculations. In addition, the corresponding errors of the numerical results are computed. Novelty: the numerical simulation demonstrates the reliability and efficiency of the Fibonacci collocation method. The proposed method is very effective, simple, and suitable for solving functional integro-differential equations. Motivation for using the Fibonacci collocation method is that it gives highly accurate solutions.
ISSN:1687-2762
1687-2770
DOI:10.1186/s13661-025-02078-8
Baliabidea:Advanced Technologies & Aerospace Database