Concerning an analytical solution of some families of Kepler’s transcendental equation

Abstract

The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.

The Special Trans Functions Theory for the Degree of Nuclear Fuel Burn-Up Estimation

“…(3)) is solvable using the Special Tran Function Theory [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions.…”

“…Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions. Examples of STFT application are shown in articles concerning the closed-form solution genesis in: the theory of neutron slowing down [ [6], [7], [16]], the nonlinear circuit theory [ [8], [16], [22]], the linear transport theory [ [9], [16], [20]], the Hopfield neuron analysis [11], some families of transcendental equations analysis [ [12], [16], [17]], the solar cell theoretical analysis [ [13], [18], [22]], the Plutonium temperature estimation [14], the ambient temperature estimation [ [15], [16]], the Lambert transcendental equations analysis [ [16], [17], [23]], as well as in the problem in the engineering materials [19], [21], [22]], etc.…”

On an exact analytical solution in Weibull probability distribution domain

“…In an exact way the number of accurate digits in the practical applicable V > or V < wind speed is in accordance with physical requirements of exactness. Accordingly, the final form of solutions (21)-(24) continues to stay in the domain of an analytical form, regardless of the number of accurate digits in the numerical structure of V > or V < wind speed which are obtained by computer calculation [ [5], [6], [11]]. …”

“…Examples of STFT application are shown in papers concerning the calculation of the closed-form solutions in: some families of transcendental equations [11], Lambert transcendental equation [16], problem in engineering materials [18], theory of neutron slowing [5][6], linear transport theory [ [8], [15], [19]], Plutonium temperature estimation [13], temperature estimation [14], nonlinear circuit theory [7] and Hopfield neuron analysis [10], as well as solar cell analysis [12,17] etc.…”

Obtaining an analytical STFT closed form solution to the solar cell junction ideality factor using the maximum power point characteristics

“…V CONCLUSIONS From the previous sections and listed references it is obvious that the Special Tran Functions Theory is a consistent general approach to solving transcendental equations in solar cell circuit domain. This means that in some manner we can obtain various Special Tran Functions (for example, [20], [22], [34] etc.). A new formulae within solar cell theory, equations (24), being derived in the paper, using the STFT, is valid in the numerical sense (See Table 1).…”