What question did this study set out to answer?

The aim is to develop a numerical method for effectively solving first-order nonlinear Volterra-Fredholm integro-differential equations.

August 11, 2026Open Access

A Numerical Method for Solving First-Order Nonlinear Volterra-Fredholm Integro-differential Equations Using Power Series Polynomials

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Numerical method solves first-order nonlinear Volterra-Fredholm integro-differential equations, indicating high accuracy and efficiency.

The aim is to develop a numerical method for effectively solving first-order nonlinear Volterra-Fredholm integro-differential equations.
Approximated the equations using power series polynomials.
Transformed the integro-differential equations into a system of algebraic equations.
Utilized the collocation approach for solving the algebraic equations.
The method showed rapid convergence and high accuracy with minimal computational effort.
Numerical examples demonstrated excellent agreement with exact solutions.
The approach is competitive with other existing methods.

D et al. (2026) studied this question.

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