On the Approximate Solution of a Nonlinear Singular Integral Equation
In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.
[1] E.G. Ladopoulas, "On the numerical evaluation of the general type of
finite-part singular integrals and integral equations used in fracture
mechanics", J. Engng. Fract. Mech. 31, 1988, pp.315-337.
[2] E.G. Ladopoulas, "On a new integration rule with the Gegenbauer
polynomials for singular integral equations used in the theory of
elasticity", Ing. Archiv 58, 1988, pp.35-46.
[3] E.G. Ladopoulas, "On the numerical solution of the finite-part singular
integral equations of the first and the second kind used in fracture
mechanics", Comput. Methods Appl. Mech. Engng. 65, 1987, pp.253-
266.
[4] E.G. Ladopoulas, "On the solution of the finite-part singular integrodifferential
equations used in two-dimensional aerodynamics", Arch.
Mech. 41, 1989, pp.925-936.
[5] E.G. Ladopoulas, "The general type of finite-part singular integrals and
integral equations with logarithmic singularities used in fracture
mechanics", Acta Mech. 75, 1988, pp.275-285.
[6] E.G. Ladopoulas, V.A. Zisis, "Nonlinear finite-part singular integral
equations arising in two-dimensional fluid mechanics", J. Nonlinear
Analysis, 42, 2000, pp.277-290.
[7] E.G. Ladopoulas, "Nonlinear singular integral equations
elastodynamics by using Hilbert Transformations", J. Nonlinear
Analysis: Real World Applications 6 2005, pp.531-536.
[8] L. Bers and L. Nirenberg , "On a representation for linear elliptic
systems with discontinuous coefficients and its applications",
Convegno intern sulle equaz. lin. alle deriv. parz; Triest, 1954,
pp.111-140.
[9] B.V. Bojarskii, "Quasiconformal mappings and general structural
properties of system of nonlinear elliptic in the sense of Lavrentev",
Symp. Math.18, 1976, pp.485-499.
[10] E. Lanckau and W. Tutschke, Complex analysis, methods, trends and
applications. Pergamon Press, London, 1985.
[11] V.N. Monahov, Boundary value problems with free boundaries for
elliptic systems. Nauka, Novosibirsk , 1977.
[12] A.S. Mshim Ba and W. Tutschke, Functional-analytic methods in
complex analysis and applications to partial differential equations.
World Scientific, Singapore, New Jersey, London, 1990.
[13] W. Tutschke," Lözung nichtlinearer partieller Differentialgleichungssysteme
erster Ordnung inder Ebene cluch verwendung
einer komplexen Normalform", Mat. Nachr. 75, 1976, pp.283-298.
[14] I.N. Vekua, Generalized analytic functions. Pergamon Press, London,
1962.
[15] A. Zygmund and A.P. Calderon A.P, "On the existence of singular
integrals", Acta Mathematica 88, 1952, pp.85- 139.
[16] A.I. Gusseinov and H.S. Muhtarov, Introduction to the theory of
nonlinear singular integral equations. Nauka, Moscow, 1980.
[1] E.G. Ladopoulas, "On the numerical evaluation of the general type of
finite-part singular integrals and integral equations used in fracture
mechanics", J. Engng. Fract. Mech. 31, 1988, pp.315-337.
[2] E.G. Ladopoulas, "On a new integration rule with the Gegenbauer
polynomials for singular integral equations used in the theory of
elasticity", Ing. Archiv 58, 1988, pp.35-46.
[3] E.G. Ladopoulas, "On the numerical solution of the finite-part singular
integral equations of the first and the second kind used in fracture
mechanics", Comput. Methods Appl. Mech. Engng. 65, 1987, pp.253-
266.
[4] E.G. Ladopoulas, "On the solution of the finite-part singular integrodifferential
equations used in two-dimensional aerodynamics", Arch.
Mech. 41, 1989, pp.925-936.
[5] E.G. Ladopoulas, "The general type of finite-part singular integrals and
integral equations with logarithmic singularities used in fracture
mechanics", Acta Mech. 75, 1988, pp.275-285.
[6] E.G. Ladopoulas, V.A. Zisis, "Nonlinear finite-part singular integral
equations arising in two-dimensional fluid mechanics", J. Nonlinear
Analysis, 42, 2000, pp.277-290.
[7] E.G. Ladopoulas, "Nonlinear singular integral equations
elastodynamics by using Hilbert Transformations", J. Nonlinear
Analysis: Real World Applications 6 2005, pp.531-536.
[8] L. Bers and L. Nirenberg , "On a representation for linear elliptic
systems with discontinuous coefficients and its applications",
Convegno intern sulle equaz. lin. alle deriv. parz; Triest, 1954,
pp.111-140.
[9] B.V. Bojarskii, "Quasiconformal mappings and general structural
properties of system of nonlinear elliptic in the sense of Lavrentev",
Symp. Math.18, 1976, pp.485-499.
[10] E. Lanckau and W. Tutschke, Complex analysis, methods, trends and
applications. Pergamon Press, London, 1985.
[11] V.N. Monahov, Boundary value problems with free boundaries for
elliptic systems. Nauka, Novosibirsk , 1977.
[12] A.S. Mshim Ba and W. Tutschke, Functional-analytic methods in
complex analysis and applications to partial differential equations.
World Scientific, Singapore, New Jersey, London, 1990.
[13] W. Tutschke," Lözung nichtlinearer partieller Differentialgleichungssysteme
erster Ordnung inder Ebene cluch verwendung
einer komplexen Normalform", Mat. Nachr. 75, 1976, pp.283-298.
[14] I.N. Vekua, Generalized analytic functions. Pergamon Press, London,
1962.
[15] A. Zygmund and A.P. Calderon A.P, "On the existence of singular
integrals", Acta Mathematica 88, 1952, pp.85- 139.
[16] A.I. Gusseinov and H.S. Muhtarov, Introduction to the theory of
nonlinear singular integral equations. Nauka, Moscow, 1980.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:49500", author = "Nizami Mustafa and C. Ardil", title = "On the Approximate Solution of a Nonlinear Singular Integral Equation", abstract = "In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.
", keywords = "Approximate solution, Fixed-point principle,Nonlinear singular integral equations, Vekua integral operator", volume = "6", number = "10", pages = "1376-7", }
