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Approximate solution of singular integro‐differential equations in elastic contact problems
Author(s) -
Sankar T. S.,
Hoa S. V.,
Fabrikant V. I.
Publication year - 1982
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620180403
Subject(s) - mathematics , mathematical analysis , algebraic equation , exact solutions in general relativity , power series , differential equation , plane (geometry) , boundary value problem , fortran , numerical analysis , series (stratigraphy) , ordinary differential equation , singular integral , boundary (topology) , integral equation , nonlinear system , geometry , computer science , paleontology , physics , quantum mechanics , biology , operating system
A method for the numerical solution of singular integro‐differential equations is proposed. The approximate solution is sought in the form of the sum of a power series with unknown coefficients multiplied by a special term which controls the appropriate solution behaviour near and at the edges of the interval. The coefficients are to be determined from a system of linear algebraic equations. The method is applied to the solution of a contact problem of a disk inserted in an infinite elastic plane. Exact analytical solution is obtained for the particular case when the disk is of the same material as the plane. Comparison is made between the exact and the approximate solutions as well as with the solutions previously available in literature. The stability and the accuracy of the present method is investigated under variation of the parameters involved. The applicability of the method to the case when the boundary conditions for the unknown function are nonzero is discussed along with an illustrative example. A FORTRAN subroutine for the numerical solution of singular integro‐differential equations is also provided.