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Zbl 1235.80048
Waziri, Mohammed Yusuf; Leong, Wah June; Hassan, Malik Abu; Monsi, Mansor
A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems. (English)
[J] Math. Probl. Eng. 2011, Article ID 467017, 12 p. (2011). ISSN 1024-123X; ISSN 1563-5147/e

Summary: The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a new approach that was based on approximating the Jacobian inverse into a diagonal matrix by means of variational technique. Numerical results on well-known benchmarks integral equations involved in the radiative transfer authenticate the reliability and efficiency of the approach. The fact that the proposed method can solve the integral equations without function derivative and matrix storage can be considered as a clear advantage over some other variants of Newton's method.

MSC 2000:: *80M25 Other numerical methods
80A20 Heat and mass transfer
65R20 Integral equations (numerical methods)

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Zentralblatt MATH Berlin [Germany]