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Comment: Reply to the comment on the transcendental method. (English) Zbl 0858.65134

Summary: Using an unconventional mathematical approach and analysis of the precision of solution by a new formula for the representation of number in the transcendantal method, we indicate that the objection given in the comment of P. Miranovic [ibid. 28, No. 14, 4189-4190 (1995; reviewed above)] most probably shows a lack of understanding and misapprehension. Undoubtedly, the transcendental equation of the neutron slowing down has an analytic closed-form solution. This solution is exact according to the new closed-form representation of numbers with the desired accuracy. The numerical results, obtained for different magnitudes of the transcendental parameter \(B(u)\), support the validity and basic principles of the transcendental method.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45H05 Integral equations with miscellaneous special kernels
82D75 Nuclear reactor theory; neutron transport

Citations:

Zbl 0858.65133
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