On the numerical solution of singular integro-differential equations

Authors:
N. I. Ioakimidis and P. S. Theocaris

Journal:
Quart. Appl. Math. **37** (1979), 325-331

MSC:
Primary 65R20

DOI:
https://doi.org/10.1090/qam/548991

MathSciNet review:
548991

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A method of numerical solution of a sufficiently wide class of Cauchy-type singular integrodifferential equations along a straight finite interval is presented. This method consists of approximating the integrals in such an equation by using appropriate numerical integration rules and appropriately-selected collocation points and reducing such an equation to a system of linear algebraic equations. This technique constitutes a direct generalization of the corresponding methods of numerical solution of Cauchy-type singular integral equations and presents some advantages over the classical Multhopp method of numerical solution of Cauchy-type singular integrodifferential equations, to which it reduces in some special cases. An application to a specific equation is also made.

**[1]**A. I. Kalandiya,*Approximate solution of a class of singular integral equations*, Dokl. Akad. Nauk SSSR**125**, 715-718 (1959) (English translation available through the British Library-Lending Division: RTS 8730, 1974)**[2]**A. I. Kalandiya.*Mathematical methods of two-dimensional elasticity*, Mir Publishers, Moscow, 1973 (English translation: 1975) MR**0400846****[3]**F. Erdogan and G. D. Gupta,*On the numerical solution of singular integral equations*, Quart. Appl. Math.**30**, 525-534 (1972) MR**0408277****[4]**P. S. Theocaris and N. I. Ioakimidis,*Numerical integration methods for the solution of singular integral equations*, Quart. Appl. Math.**35**, 173-183 (1977) MR**0445873****[5]**N. I. Ioakimidis and P. S. Theocaris,*On the numerical evaluation of Cauchy principal value integrals*, Rev. Roum. Sci. Techn.-Sér. Mécan. Appl.**22**, 803-818 (1977) MR**0483321****[6]**N. I. Ioakimidis and P. S. Theocaris,*On the numerical solution of a class of singular integral equations*, J. Math. Phys. Sci.**11**, 219-235 (1977) MR**0483590****[7]**P. S. Theocaris,*On the numerical solution of Cauchy-type singular integral equations*, Serdica, Bulgar. Math. Publ.**2**, 252-275 (1976) MR**0448968****[8]**P. S. Theocaris and N. I. Ioakimidis,*On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities*, Zeit. Ang. Math. Phys. (ZAMP)**28**, 1085-1098 (1977) MR**0464623****[9]**P. S. Theocaris and N. I. Ioakimidis,*Numerical solution of Cauchy type singular integral equations*, Trans. Acad. Athens**40**, 1-39 (1977) MR**0659483****[10]**N. I. Ioakimidis and P. S. Theocaris,*The numerical evaluation of a class of generalized stress intensity factors by use of the Lobatto-Jacobi numerical integration rule*, Int J. Fract.**14**(1978) (in press) MR**599793****[11]**P. S. Theocaris and G. Tsamasphyros,*Numerical solution of systems of singular integral equations with variable coefficients*, J. Applicable Anal.**9**, 37-52 (1979) MR**536690****[12]**H. Multhopp,*Die Berechnung der Auftriebsverteilung von Tragflügeln*, Luftfahrtforschung**15**, 153-166 (1938)**[13]**S. M. Sharfuddin,*A two-dimensional discontinuous boundary-value problem for circular regions and Prandtl's integral equation*, Acta Mech.**4**, 374-381 (1967)**[14]**M. Stippes, H. B. Wilson, Jr. and F. N. Krull,*A contact stress problem for a smooth disk in an infinite plate*, Proc. 4th U.S. Nat. Congr. Appl. Mech.**2**, 799-806 (1962) MR**0152183****[15]**S. Krenk,*On the use of the interpolation polynomial for solutions of singular integral equations*, Quart. Appl. Math.**32**, 479-484 (1975) MR**0474919**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
65R20

Retrieve articles in all journals with MSC: 65R20

Additional Information

DOI:
https://doi.org/10.1090/qam/548991

Article copyright:
© Copyright 1979
American Mathematical Society