 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| A.V. Saakyan, "Quadrature Formulas of Maximum Algebraic Accuracy for Cauchy Type Integrals with Complex Exponents of the Jacobi Weight Function," Mech. Solids. 47 (6), 695-699 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
6 |
Pages |
695-699 |
| DOI |
10.3103/S002565441206012X |
| Title |
Quadrature Formulas of Maximum Algebraic Accuracy for Cauchy Type Integrals with Complex Exponents of the Jacobi Weight Function |
| Author(s) |
A.V. Saakyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshal Baghramian ave., 24B, Erevan, 375019 Republic of Armenia, avsah@mechins.sci.am) |
| Abstract |
The present paper presents a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Hölder function by the weight function (1−x)α(1+x)β (Reα,Reβ>−1) of orthogonal Jacobi polynomials. It is shown that at the roots of the function of the second kind corresponding to the Jacobi polynomial Pn(α,β)(x), the quadrature formula with n nodes gives the exact value of a Cauchy type integral for an arbitrary polynomial of order k≤2n. This formula was tested when solving several contact and mixed problems of the theory of elasticity. |
| Keywords |
singular integral, Jacobi polynomial, quadrature formula, theory of elasticity, crack, inclusion |
| References |
| 1. | A. V. Saakyan,
"Numerical Method for Solving Singular Integral Equations of the Second Kind
with a Complex Coefficient,"
Dokl. NAN RA
97 (4), 32-36 (1997). |
| 2. | N. Kh. Arutyunyan,
"Contact Problem for a Half-Plane with Elastic Reinforcement,"
Prikl. Mat. Mekh.
32 (4), 632-646 (1968)
[J. Appl. Math. Mech. (Engl. Transl.)
32 (4), 652-665 (1968)]. |
| 3. | H. Bateman and A. Erdélyi,
Higher Transcendental Functions. Vol. 2:
Bessel Functions, Functions of Parabolic Cylinder, Orthogonal Polynomials
(McGraw-Hill, 1953; Nauka, Moscow, 1974). |
| 4. | V. I. Krylov,
Approximate Computations of Integrals
(Nauka, Moscow, 1967)
[in Russian]. |
| 5. | A. A. Korneichuk,
"Quadrature Formulas for Singular Integrals,"
in Numerical Methods for Solving Differential and Integral Equations and Quadrature Formulas
(Nauka, Moscow, 1964), pp. 64-74. |
| 6. | A. V. Saakyan,
"The Method of Discrete Singularities for Solutions of Singular Integral
and Integro-Differential Equations,"
Proc. A. Razmadze Math. Inst., Georgia
156, 101-111 (2011). |
| 7. | A. V. Andreev,
"Direct Numerical Method for Solving Singular Integral Equations of the First Kind
with Generalized Kernels,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 126-146 (2005)
[Mech. Solids (Engl. Transl.)
40 (1), 104-119 (2005)]. |
| 8. | V. N. Akopyan and A. V. Saakyan,
"Numerical Analysis of Mixed Problem for Compound Plane with a Thin Rigid Inclusion
by the Method of Discrete Singlarities,"
in Problems of Optimal Control, Stability, and Strength of Mechanical Systems
(Izdat. ErGU, Erevan, 1997). |
| 9. | A. V. Saakyan and L. L. Dashtoyan,
"On One Problem for Compound Plane with Crack and Inclusion
with Existence of Temperature Field,"
in Proc. 5th Intern. Cong. on Thermal Stresses and Related Topics.
Blacksburg, VA, 2003,
pp. TM-4-1-1-TM-4-1-4. |
| 10. | V. N. Akopyan and A. V. Saakyan,
"On One Mixed Problem for an Elastic Wedge Weakened by a Crack,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 66-78 (1999)
[Mech. Solids (Engl. Transl.)]. |
| 11. | V. N. Akopyan and A. V. Saakyan,
"The Stress State of a Homogeneous Elastic Plane with a Star-Shaped
Crack under Mixed Boundary Conditions on the Crack Faces,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 106-113 (1999)
[Mech. Solids (Engl. Transl.)]. |
|
| Received |
18 July 2012 |
| Link to Fulltext |
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