A new method for the numerical solution of Fredholm integral equations of the first kind

✍ Scribed by Owen T. Hanna; Lee F. Brown

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 662 KB
• Volume: 46
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(91)80066-8

✦ Synopsis

INTRODUCTEON A linear Frcdhofm equation ol the first kind is defined by the ~XpE&3?l Here g(x) and K{x, c) are normally known functions, while it is desired to calculate #I. Although K(x, t) is usually known with high pwekkm, often g(x) is not. Examptes of&s kind of problem ial chemistry and chemical engineering include the forty-year effort to secure site-energy distributions from adsorption isotherms (e.g., Z&adz an& h&yers, 1979; Brawn and Travis, 1984) and the more recent attempts to obtain them from temperature~~rogrammed dcsorption spectra jBrittcn ef ai., ISS3); deriving one type of pore-size distribution from Wicke-Kalienbach diffusion experiments (Brown and Travis, 1983) and another from NMR experimeats (Brown et a!., 19821; using chemically reacting tracers ta measure temperature prafilot?s in ptug-flow systems ~~hembur~ar et ul., i991), Such problems also wcw frequently in other f&Ids of engineering and science (Allison, 19TQj. It is well known that Fredholm integral equations of the first kind, in contrast to those of the second kind, are intrins-&ally ill-posed and aze often quite dif&nlt to s&e numerically. Almost all such equations (even the Linear variety) are