Airfoil polynomials for solving integro-differential equations with logarithmic kernel

Mennouni, Abdelaziz

doi:10.1016/j.amc.2012.06.004

Cited by 7 publications

(2 citation statements)

References 5 publications

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“…Moreover, the author used a sequence of orthogonal finite rank projections to approximate the solution of singular integral equations of the second kind with Cauchy kernel. The main idea of [10] is to propose a collocation method for solving singular integro-differential equations with logarithmic kernel using airfoil polynomials. The goal of [9] is to numerically solve the Cauchy integro-differential equations using the projection method based on the Legendre polynomials.…”

Section: Introductionmentioning

confidence: 99%

Three methods to solve two classes of integral equations of the second kind

2022

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Three methods to solve two classes of integral equations of the second kind are introduced in this paper. Firstly, two Kantorovich methods are proposed and examined to numerically solving an integral equation appearing from mathematical modeling in biology. We use a sequence of orthogonal nite rank projections. The rst method is based on general grid projections. The second one is established by using the shifted Legendre polynomials. We establish a new convergence analysis and we prove the associated theorems. Secondly, a new Nystrom method is introduced for solving Fredholm integral equation of the second kind.

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Section: Introductionmentioning

confidence: 99%

Three methods to solve two classes of integral equations of the second kind

2022

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“…For example, it blue can be used to study the Brown displacement and thermal diffusion of suspended grain in heterogeneous fluid. When determining the profile of airfoil, the integro-differential equation can be used to calculate the effect of circulation, lift and resistance of the air [10]. Because of their application values, integro-differential equations are essential and significant research subjects.…”

Section: Introductionmentioning

confidence: 99%

The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations

Wang¹

2020

AAMM

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In this paper, we solve linear parabolic integral differential equations using the weak Galerkin finite element method (WG) by adding a stabilizer. The semidiscrete and fully-discrete weak Galerkin finite element schemes are constructed. Optimal convergent orders of the solution of the WG in L 2 and H 1 norm are derived. Several computational results confirm the correctness and efficiency of the method.

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Improvement by projection for integro‐differential equations

Mennouni

2020

Math Methods in App Sciences

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The aim of this work is to establish an improved convergence analysis via Kulkarni method to approximate the solution of an integro‐differential equation in . We prove the following convergence orders: Kulkarni order is , and Kulkarni iterated order is . The present study extends and improves earlier results in the literature. A numerical example illustrates the theoretical results and shows the effectiveness of the method.

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Airfoil polynomials for solving integro-differential equations with logarithmic kernel

Cited by 7 publications

References 5 publications

Three methods to solve two classes of integral equations of the second kind

Three methods to solve two classes of integral equations of the second kind

The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations

Improvement by projection for integro‐differential equations

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