Numerical Algorithms· 2026Q1
A class of efficient linearly implicit methods based on TASE operators for Volterra integral equations
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- Q1SCImago
- 2026year
Short summary
A new family of numerical methods combining Runge-Kutta, TASE operators, backward differentiation, and Gregory quadrature achieves theoretical convergence and stability for Volterra integral equations.
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Key points
- Presents a new family of numerical methods for Volterra integral equations of the second kind.
- Combines Runge-Kutta methods, TASE operators, backward differentiation formulas, and Gregory quadrature rules.
- Numerical experiments confirm theoretical convergence orders and linear stability.
- Demonstrates efficiency for solving stiff problems.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract This paper presents a family of numerical methods for the solution of Volterra integral equations of the second kind. The proposed approach combines a class of Runge–Kutta methods for ordinary differential equations with TASE operators, backward differentiation formulas, and Gregory quadrature rules. Numerical experiments confirm the theoretical results on convergence order and linear stability, demonstrating the efficiency of the proposed methods for the solution of stiff problems.
The authors' abstract, as published at the source. Numerical Algorithms, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics