Abstract
As stated in the previous chapter, an integral equation is the equation in which the unknown function u(x) appears inside an integral sign [1–5]. The most standard type of integral equation in u(x) is of the form
where g(x) and h(x) are the limits of integration, λ is a constant parameter, and K(x, t) is a known function, of two variables x and t, called the kernel or the nucleus of the integral equation. The unknown function u(x) that will be determined appears inside the integral sign. In many other cases, the unknown function u(x) appears inside and outside the integral sign. The functions f(x) and K(x, t) are given in advance. It is to be noted that the limits of integration g(x) and h(x) may be both variables, constants, or mixed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C.D. Green, Integral Equations Methods, Barnes and Noble, New York, (1969).
H. Hochstadt, Integral Equations, Wiley, New York, (1973).
A. Jerri, Introduction to Integral Equations with Applications, Wiley, New York, (1999).
R. Kanwal, Linear Integral Equations, Birkhauser, Boston, (1997).
R. Kress, Linear Integral Equations, Springer, Berlin, (1999).
A.M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, (1997).
K. Maleknejad and Y. Mahmoudi, Taylor polynomial solution of highorder nonlinear Volterra-Fredholm integro-differential equations, Appl. Math. Comput. 145 (2003) 641–653.
A.M. Wazwaz, A reliable treatment for mixed Volterra-Fredholm integral equations, Appl. Math. Comput., 127 (2002) 405–414.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2011 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wazwaz, AM. (2011). Introductory Concepts of Integral Equations. In: Linear and Nonlinear Integral Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21449-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-21449-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21448-6
Online ISBN: 978-3-642-21449-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)