Use iteration to solve the recurrence relationan=an−1+nwitha0=4. Question: an=an−1+n a0=4 Iteration Method: We use the iteration approach to solve recurrence relations. Using this approach, the smaller terms are repeatedly substituted until the base condition is met....
We introduce a new approach to the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique, and we develop a novel termination condition in terms of the approximants. With the help of this alternative termination condition ...
Using the above property, we describe the new method to generate the coefficients of the ortho- normal polynomials in terms of the Chebyshev weight below. We use the three term recurrence 1 1 1 where satisfies the ortho-normality. Because ...
Section2.4characterizes the overall iterative algorithm as a fixed-point policy-iteration-type method, allowing for reformulations of the original problem and results pertaining to the solutions. The necessary matrix and graph-theoretic definitions and results needed are collected in AppendixAfor the reade...
He-Laplace methodHe's polynomialsKdV equationInverse laplace transformThe goal of this study deals with an effective approach to achieve the approximate solution of nonlinear partial differential equations (NPDE's). This approach exempts the calculation of integration in recurrence relation, and the ...
The method consists of generating a sequence of functions by a recurrence relation. The initial function used is arbitrary. The solution of the nonlinear ordinary differential equation is approximated. It is found that any constants of integration are not used in evaluating th e { Tn }. This ...
It is involved in mathematical practice not only as a privileged object, but also as method, in reasoning by recurrence. Reiteration is the entry into the differential territory of iteration; the possibility of thinking differences outside the field of sensible repetition. This point is essential ...
In this section, the additive synthesis method mentioned above is adopted after the subjective weight and the objective weight have been obtained by the corresponding weighting methods. For the subjective weight, there is the Delphi method [8], the consistency theorem method [34], and so on; fo...
Currently, in the study of flood classification, the commonly used methods to determine the weight of evaluation indexes are the Delphi method [8], the consistency theorem method [7,34], the entropy weight method [24] and the projection pursuit method [35,36], which can be divided into ...