Introductory Concepts of Integral Equations

Abdul-Majid Wazwaz ()
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Abdul-Majid Wazwaz: Saint Xavier University

Chapter Chapter 2 in Linear and Nonlinear Integral Equations, 2011, pp 33-63 from Springer

Abstract: 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 2.1 $$u\left( x \right) = f\left( x \right) + \int_{g\left( x \right)}^{h\left( x \right)} {K\left( {x,t} \right)u\left( t \right)dt,} $$ 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.

Keywords: Integral Equation; Boundary Value Problem; Singular Integral Equation; Integral Sign; Initial Value Problem (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-21449-3_2

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