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February 26, 2026Open Access

Collocation-Variational Approaches to Solve the Volterra Integral Equations of the First Kind Numerically

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Authors

MBM. V. Bulatov

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Overview

Variational methods solve Volterra integral equations in numerical experiments, indicating effective algorithm design.

Key Points

  • This research aims to identify and solve linear Volterra equations of the first kind using numerical methods.
  • Identified a class of linear Volterra equations with a single solution.
  • Proposed collocation-variational methods for numerical solutions.
  • Formulated the problem as quadratic programming with Lagrange multipliers analysis.
  • Detailed examination of sufficiently simple third-order methods.
  • Developed algorithms yield an underdetermined system of linear algebraic equations.
  • Conditions for minimum objective function leads to effective solving of integral equations.
  • Presented calculation results for various test problems demonstrating method efficacy.

Cite This Study

M. V. Bulatov (2025) studied this question.

synapsesocial.com/papers/699f95571bc9fecf3dab2ef2https://doi.org/10.7868/s303453325010016
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