On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z ″ = λ z , where λ is a function in C ∞ . We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equatio...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-05, Vol.216 (5), p.1375-1382
Main Author: Misir, Adil
Format: Article
Language:English
Subjects:
Acoustic scattering problem
Construction
Differential equation
Differential equations
Exact sciences and technology
Global analysis, analysis on manifolds
Helmholtz equation
Inverse
Iterative methods
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Riccati differential equation
Scattering
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Wave equations
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Summary:In this paper we present an “iteration” technique for a class of differential equation having the form z ″ = λ z , where λ is a function in C ∞ . We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition λ 2 n - 1 λ 2 n - 2 = λ 2 n - 3 λ 2 n - 4 ≔ β . Then we give a simple application of this technique to inverse conductive scattering problem for an inhomogeneous spherical medium.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.03.008