Volterra integral equations: An approach based on Lipschitz-continuity

Article Mathematics, Applied

Bernstein operator method for approximate solution of singularly perturbed Volterra integral equations

Fuat Usta et al.

Summary: This paper presents and tests an algorithm for the approximate solution of singularly perturbed Volterra integral equations using the Bernstein approximation technique. The method of computing the numerical approximation is properly demonstrated and exemplified in matrix notation. Additionally, error bounds and convergence associated with the numerical scheme are investigated, and specific examples are provided to compare the reliability and numerical capability of the introduced scheme with other techniques.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2022)

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Article Mathematics, Applied

Numerical solution of Volterra integral equations via Szasz-Mirakyan approximation method

Fuat Usta et al.

Summary: Szasz-Mirakyan operators are utilized in this study as a powerful tool to approximate functions on the unbounded interval [0,infinity). A numerical solution for Volterra integral equations is proposed, with a provided numerical scheme and estimation of error bound of solution. Numerical experiments demonstrate the performance of the new algorithm constructions in one-dimensional approximation.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Economics

An Integral Equation Representation for Optimal Retirement Strategies in Portfolio Selection Problem

Junkee Jeon et al.

Summary: This paper studies the consumption and portfolio selection problem of an economic agent with an early retirement option. By deriving integral equations and numerical solutions, the optimal retirement strategies and economic implications are discussed. The study provides insights into the optimal retirement decisions for individuals with a finite lifespan.

COMPUTATIONAL ECONOMICS (2021)

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Article Mathematics, Interdisciplinary Applications

Functional sensitivity analysis of ruin probability in the classical risk models

Fatah Cheurfa et al.

Summary: This paper investigates the impact of uncertain input parameters on the ruin probability in insurance risk models through sensitivity analysis and Taylor-series expansion methodology. By calibrating probability distributions with available data, a computational model is established to estimate ruin probability under uncertain rates, providing a new sensitivity estimate. Numerical experiments are presented to demonstrate the potential of the proposed approach.

SCANDINAVIAN ACTUARIAL JOURNAL (2021)

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Article Engineering, Electrical & Electronic