Solving Volterra integral equations via fourth-degree hat functions

Mohammed, Jehad K.; Khudair, Ayad R.

doi:10.1016/j.padiff.2023.100494

Cited by 7 publications

(2 citation statements)

References 39 publications

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“…The outcomes, portrayed with clarity and rigor, underline the method's efficacy in generating solutions that align closely with exact results. Through this comprehensive exposition, the paper underscores the capacity of the HJmethod to surmount the intricate challenges posed by these equations, heralding a new era of analytical solutions that transcend existing limitations [6,7].…”

Section: Introductionmentioning

confidence: 97%

A New Analytical Approach to First Kind Volterra Integral Equations

Hussein,

jassim,

Elzaki

et al. 2023

Preprint

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A significant group of mathematical issues known as Volterra integral equations appear in numerous scientific and engineering applications. These equations are inherently nonlinear and complicated, making analytical solution difficult. In order to solve Volterra integral equations of the first class, a novel analytical technique known as the Hussein Jassim Method (HJ-method) is presented in this research work. The Volterra integral equations are introduced mathematically in the first section of the study, which also emphasizes their importance in simulating real-world processes. The novel method’s algorithm is then described, followed by an analysis. We also research the novel method’s convergence characteristics and the circumstances under which it produces trustworthy results. We provide a number of Volterra integral equation examples to show the potency of this approach. In the end, the new method has proven to be effective and efficient in solving first-kind Volterra integral equations. The method has produced satisfactory results, with the obtained solution closely approximating the exact solution. These findings indicate the capability of this method to address the mathematical and technical challenges associated with solving Volterra integral equations. This also makes it possible to use the new technique in other relevant practical contexts.

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Section: Introductionmentioning

confidence: 97%

A New Analytical Approach to First Kind Volterra Integral Equations

Hussein,

jassim,

Elzaki

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Nonlinear integral equations are mathematical equations that involve both integrals and nonlinear functions [1,2]. These equations play a crucial role in various scientific and engineering fields, describing phenomena where the relationship between variables is not linear [3][4][5]. The general form of a nonlinear integral equation can be represented as:…”

Section: Introductionmentioning

confidence: 99%

An iterative method for robust solutions to nonlinear Volterra integral equations: Stability, convergence, and practical applications

Azure

2024

Math. Syst. Sci.

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<p>The paper introduces an iterative method for solving nonlinear Volterra integral equations and analyzes its convergence, stability, and application through examples. It expresses the general nonlinear Volterra integral equation as a series and decomposes the nonlinear operator to derive a recursive formula for the proposed iterative method. The method ensures absolute and uniform convergence, with stability analysis conducted to ensure bounded errors in the presence of perturbations. Convergence analysis utilizes the Lipschitz condition, demonstrating the uniform convergence of the solution series. Illustrative examples, including power nonlinearity and trigonometric functions, validate the stability and convergence of the method. Through graphical representations, convergence analyses for specific integral equations demonstrate the method’s effectiveness and applicability in solving diverse nonlinear integral equations. Overall, the paper contributes a robust iterative method with insights into its stability and convergence properties, supported by practical examples.</p>

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The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

Alquran¹

2023

Partial Differential Equations in Applied Mathematics

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Solving Volterra integral equations via fourth-degree hat functions

Cited by 7 publications

References 39 publications

A New Analytical Approach to First Kind Volterra Integral Equations

A New Analytical Approach to First Kind Volterra Integral Equations

An iterative method for robust solutions to nonlinear Volterra integral equations: Stability, convergence, and practical applications

The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

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