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Numerical solution of integral equations with logarithmic‐, Cauchy‐ and Hadamard‐type singularities
Author(s) -
Kabir H.,
Madenci E.,
Ortega A.
Publication year - 1998
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/(sici)1097-0207(19980228)41:4<617::aid-nme301>3.0.co;2-k
Subject(s) - mathematics , hadamard transform , logarithm , piecewise , gravitational singularity , mathematical analysis , cauchy's integral formula , cauchy distribution , type (biology) , singular integral , polynomial , residue theorem , integral equation , cauchy problem , initial value problem , ecology , biology
This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic‐ and Hadamard‐type singularities. For completeness and continuity, the evaluation of the weights for logarithmic‐, Cauchy‐ and Hadamard‐type singularities are given explicitly. Numerical results concerning logarithmic‐ and Hadamard‐type singular integral equations are compared with the known solutions. The solution of Cauchy‐type singular integral equations was discussed in detail in a previous study by Miller and Keer. © 1998 John Wiley & Sons, Ltd.