On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity. (English) Zbl 0627.73018
A new technique is proposed for the numerical solution of the Cauchy-type singular integral equations, by using the well known Gegenbauer polynomials. A large class of problems of mathematical physics, and especially several plane and antiplane elasticity problems, not possessing closed-form solutions, can be reduced to the solution of certain systems of such a type of singular integral equations. Also by using a certain method the new formula which is used for the numerical solution of the Cauchy-type integral equations can be extended for the general type of the finite-part singular integrals, too.
MSC:
| 74B99 | Elastic materials |
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 74R05 | Brittle damage |
Keywords:
Cauchy-type singular integral equations; Gegenbauer polynomials; plane; antiplane elasticityReferences:
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