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The Taylor series method is computationally taken long time for large order derivatives. The DTM is an iterative procedure for obtaining the analytic Taylor series solution of ordinary or partial differential equations. 52. 52 reduces to the classical differential transform. 1 Wiener Process or Brownian Motion Process A standard Wiener process (often called Brownian motion) on the interval [0,T] is a continuous time stochastic process W(t) that depends continuously on t∈[0,T] and satisfies the following properties [19–21]: 1.

1 Analytical Methods and Numerical Techniques for Solving Deterministic Neutron Diffusion and Kinetic Models This chapter provides a brief description of the analytical and n ­ umerical methods to obtain the solution for neutron point kinetic models in the nuclear dynamical system. The basic ideas of linear and nonlinear analytical methods have been introduced to solve the kinetic equation in the field of nuclear reactor dynamics using the homotopy analysis method (HAM), variational iteration method (VIM), and Adomian decomposition method (ADM).

20) n n=0 5 Mathematical Methods in Nuclear Reactor Physics where An is obtained by � 1 � dn � n N� � n ! 23) … yn+1 = −L−1R ( yn ) − L−1 ( An ) and so on. Based on the ADM, we shall consider the solution y(t) as y≅ n −1 ∑y k =0 k = ϕn with lim ϕn = y(t) n →∞ We can apply this method to many real physical problems, and the obtained results have proved to be of high accuracy. In most of the problems, the practical solution ϕn, the n-term approximation, is convergent and accurate even for small values of n.

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Nuclear Reactor Thermal-Hydraulics Vol 1 [7th Intl Meeting]


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