On nonlinear Fredholm integral equations with non‐differentiable Nemystkii operator

Hernández‐Verón, M. A.; Martínez, Eulalia

doi:10.1002/mma.5801

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…Integral equations arise in certain problems in mechanics, mathematical physics, and technology [1]. Besides that, its applications include real-world problems such as fluid mechanics, biological models, solid state physics, mathematical physics, kinetics, potential theory, electrostatics and radiative heat transfer problems [2,3]. One of the important classes of integral equations is known as Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

Ali¹,

Sulaiman²,

Saudi³

et al. 2022

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This paper is concerned with producing an efficient numerical method to solve nonlinear Fredholm integral equations using Half-Sweep Newton-PKSOR (HSNPKSOR) iteration. The computation of numerical methods in solving nonlinear equations usually requires immense amounts of computational complexity. By implementing a Half-Sweep approach, the complexity of the calculation is tried to be reduced to produce a more efficient method. For this purpose, the steps of the solution process are discussed beginning with the derivation of nonlinear Fredholm integral equations using a quadrature scheme to get the half-sweep approximation equation. Then, the generated approximation equation is used to develop a nonlinear system. Following that, the formulation of the HSNPKSOR iterative method is constructed to solve nonlinear Fredholm integral equations. To verify the performance of the proposed method, the experimental results were compared with the Full-Sweep Newton-KSOR (FSNKSOR), Half-Sweep Newton-KSOR (HSNKSOR), and Full-Sweep Newton-PKSOR (FSNPKSOR) using three parameters: number of iteration, iteration time, and maximum absolute error. Several examples are used in this study to illustrate the efficiency of the tested methods. Based on the numerical experiment, the results appear that the HSNPKSOR method is effective in solving nonlinear Fredholm integral equations mainly in terms of iteration time compared to rest tested methods.

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

Ali¹,

Sulaiman²,

Saudi³

et al. 2022

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Global convergence domains for an efficient fifth order iterative scheme

Yadav,

Singh

2023

J Math Chem

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Kurchatov-type methods for non-differentiable Hammerstein-type integral equations

et al. 2022

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We consider a generic type of nonlinear Hammerstein-type integral equations with the particularity of having non-differentiable kernel of Nemystkii type. So, in order to solve it we consider a uniparametric family of iterative processes derivative free, with the main advantage that for a special value of the involved parameter the iterative method obtained coincides with Newton’s method, that is due to the fact of evaluating the divided difference operator when the two values are the same. We perform a qualitative convergence study by choosing an auxiliary point, that allow us to obtain the existence and separation of solutions of the given equation, that is, local and semilocal convergence balls can be obtained.

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On nonlinear Fredholm integral equations with non‐differentiable Nemystkii operator

Cited by 5 publications

References 18 publications

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

Global convergence domains for an efficient fifth order iterative scheme

Kurchatov-type methods for non-differentiable Hammerstein-type integral equations

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