Numerical treatment of linear Volterra integro differential equations using variational iteration algorithm with collocation

Abstract

To numerically solve the linear Volterra integro-differential equation, this study employs fourth-kind Chebyshev polynomials and the variational iteration algorithm with collocation, which is a combination of the variational iteration strategy and collocation technique. By applying fourth-kind Chebyshev polynomials to the variational iteration method with collocation for solving Volterra integro-differential equations, mathematical problems with a broad range of multidisciplinary applications are addressed, and numerical techniques that produce more accurate and efficient results are developed. The recommended method is then used, and the fourth-kind Chebyshev polynomials generated for the given integro-differential equation serve as the trial functions for the approximation. As a result, the suggested method's significance probably goes beyond a particular equation or application, as it contributes to the larger field of mathematical modeling and numerical analysis. Research methods employing a variational iteration algorithm with collocation aim to provide general techniques that can be applied to a wide range of problems. Additionally, numerical examples were provided to highlight the applicability and dependability of the proposed methodology. The mathematical computations were carried out using the Maple 18 software.

Keywords

• Variational iteration algorithm with collocation
• Volterra integro-differential equation
• Fourth kind Chebyshev polynomials
• Approximate solutions