Preliminaries

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

Chapter Chapter 1 in Linear and Nonlinear Integral Equations, 2011, pp 3-31 from Springer

Abstract: Abstract An integral equation is an equation in which the unknown function u(x) appears under an integral sign [1&#sx20s13;7]. A standard integral equation in u(x) is of the form: 1.1 $$u\left( x \right) = f\left( x \right) + \int_{g\left( x \right)}^{h\left( x \right)} {K\left( {x,t} \right)u\left( t \right)dt,} $$ where g(x) and h(x) are the limits of integration, λ is a constant parameter, and K(x, t) is a function of two variables x and t called the kernel or the nucleus of the integral equation. The function u(x) that will be determined appears under the integral sign, and it appears inside the integral sign and outside the integral sign as well. 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; General Solution; Taylor Series; Series Solution; Laplace Transform (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-21449-3_1

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DOI: 10.1007/978-3-642-21449-3_1

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