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

Abstract

Abstract In the present paper, the Fibonacci collocation method is implemented to solve ( 1 + 1 ) $(1 + 1)$ 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.

Keywords

• Fredholm functional integro-differential equations
• Quadratic numerical technique
• Fibonacci polynomials
• Collocation points