A Survey of Numerical Methods for Integral Equations

Golberg, Michael A.

doi:10.1007/978-1-4757-1466-1_1

Cited by 41 publications

(33 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(7a) and (8a) permit the use of product integration [13,[15][16][17][18]24], and singularity subtraction [13,17,18,24],…”

Section: Jy=0mentioning

confidence: 99%

“…(7). The purely numerical solution was obtained with the aid of singularity subtraction [13,24] and simple trapezoidal integration [36]. Table 2 displays results from the approximate solution as a function of X at six spatial locations t] e [0, 1] for different values of N. Here (N/2 + 1) denotes the actual number of terms retained in the series representation shown in Eq.…”

Section: Jy=0mentioning

confidence: 99%

“…The books edited by Golberg [13,14] are particularly enlightening and should be consulted since they contain fairly extensive literature surveys on both approximate analytical and purely numerical techniques. The interested reader should also consult the fine expositions by Linz [15], Baker [16], Delves and Mohamed [17], and Atkinson [18] for numerical methods, and consult the books by Tricomi [19], Hochstadt [20], Green [21], and Porter and Stirling [22] for information concerning analytical solution methods.…”

mentioning

confidence: 99%

“…Peters [25,26] developed a simple yet insightful solution method to the airfoil equation based on reducing the airfoil equation to the solution of an Abel integral equation. More recently Golberg [13,14], and Porter and Stirling [22] have expounded on the merits of Peters' approach. In fracture mechanics [27,28], Cauchytype kernels (and stronger, i.e., (x-y)~a , a > 1) often arise.…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Galerkin solution to a regularized Cauchy singular integro-differential equation

Frankel¹

1995

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract. This paper presents a Galerkin approach for solving a regularized version of the Cauchy singular, linear integro-differential equation• Jy=o x-y subject to 0(0) = 0(1) = 0. This equation has appeared in both combined infrared gaseous radiation and molecular conduction, and elastic contact studies. A regularized formulation is produced which suggests the use of an expansion technique where the orthogonal basis functions are chosen as the Chebychev polynomials of the first kind. Accurate results, requiring a minimal computational cost, are formally documented and compared to a purely numerical solution.

show abstract

“…(7a) and (8a) permit the use of product integration [13,[15][16][17][18]24], and singularity subtraction [13,17,18,24],…”

Section: Jy=0mentioning

confidence: 99%

Section: Jy=0mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Galerkin solution to a regularized Cauchy singular integro-differential equation

Frankel¹

1995

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…Among these numerical methods are: collocation method, Galerkin method, fast method, block by block method, Gerosonli's method, least square method, Product Nystrom method, and Toeplitz matrix method. The books edited by Golberg [15], Delves and Mohamed [16], Atkinson [17,18], and Baker [19] contain these methods. More information for other methods, see [20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment of the Nonlocal Solution of Hammerstein –Volterra Integral Equation with Continuous Kernels

Kojok¹

2017

IJARCSSE

View full text Add to dashboard Cite

Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators

Mukhamedov

Khakimov

Embong

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite‐dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators.

show abstract

A Survey of Numerical Methods for Integral Equations

Cited by 41 publications

References 42 publications

A Galerkin solution to a regularized Cauchy singular integro-differential equation

A Galerkin solution to a regularized Cauchy singular integro-differential equation

Numerical Treatment of the Nonlocal Solution of Hammerstein –Volterra Integral Equation with Continuous Kernels

Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators

Contact Info

Product

Resources

About