Numerical Solution of a Class of Integral Equations Arising in a Biological Laboratory Procedure

D. A. French () and C. W. Groetsch ()
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D. A. French: University of Cincinnati
C. W. Groetsch: The Citadel

Chapter 15 in Integral Methods in Science and Engineering, Volume 2, 2010, pp 161-171 from Springer

Abstract: Abstract We discuss a numerical method for certain integral equations of the form 15.1 $$I(t) = \int^L_0 k(x, t)\rho(x)dx, \quad 0\leq t\leq T,$$ where I is a smooth increasing function with I(0) = 0, L and T are positive constants, and the kernel k(·, ·) satisfies the following assumptions: (i) k(·, ·) is continuous and bounded on [0, L] × [0, T] ? {(0, 0)}, positive on (0, L] × (0, T], and k(·, ·) ∈ C 1((0, L) × (0, T)). (ii) k(x, 0) = 0 for x > 0 and there is a positive constant k with k(0, t) ≥ k for t ∈ (0, T]. (iii) ∂1 k

Keywords: Integral Equation; Olfactory System; Tikhonov Regularization; Fredholm Integral Equation; Odor Stimulus (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4897-8_15

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DOI: 10.1007/978-0-8176-4897-8_15

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