What question did this study set out to answer?

This research aims to develop an accurate numerical method for solving fractional Volterra-Fredholm integro-differential equations using Hermite polynomials.

April 10, 2026PLoS ONEOpen Access

A highly accurate Hermite polynomial-based least-squares approach for solving fractional Volterra-Fredholm integro-differential equations

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Authors

MHMaha M. Hamood ASAbdulrahman A. Sharif KGKirtiwant P. Ghadle

Discussion

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Overview

Numerical study demonstrates a new Hermite polynomial method solves integro-differential equations, indicating high accuracy and efficiency.

Key Points

This research aims to develop an accurate numerical method for solving fractional Volterra-Fredholm integro-differential equations using Hermite polynomials.
Developed a trial solution using Hermite polynomials
Substituted the trial solution into the governing V-FFIDE
Formulated a residual function for the integrals and fractions
Minimized the squared norm of the residual to create linear equations
Validated the technique through numerical experiments on various examples
Achieved high accuracy in solving V-FFIDEs
Demonstrated computational efficiency compared to existing methods
Showed robust convergence across multiple test cases

Cite This Study

Hamood et al. (2026) studied this question.

synapsesocial.com/papers/69d893626c1944d70ce04616 https://doi.org/10.1371/journal.pone.0346080

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April 10, 2026PLoS ONEOpen Access

A highly accurate Hermite polynomial-based least-squares approach for solving fractional Volterra-Fredholm integro-differential equations

View Full Paper

Ask AI

Bookmark

Authors

MHMaha M. Hamood ASAbdulrahman A. Sharif KGKirtiwant P. Ghadle

Discussion

Member takes

Overview

Numerical study demonstrates a new Hermite polynomial method solves integro-differential equations, indicating high accuracy and efficiency.

Key Points

This research aims to develop an accurate numerical method for solving fractional Volterra-Fredholm integro-differential equations using Hermite polynomials.
Developed a trial solution using Hermite polynomials
Substituted the trial solution into the governing V-FFIDE
Formulated a residual function for the integrals and fractions
Minimized the squared norm of the residual to create linear equations
Validated the technique through numerical experiments on various examples
Achieved high accuracy in solving V-FFIDEs
Demonstrated computational efficiency compared to existing methods
Showed robust convergence across multiple test cases

Cite This Study

Hamood et al. (2026) studied this question.

synapsesocial.com/papers/69d893626c1944d70ce04616 https://doi.org/10.1371/journal.pone.0346080

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