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A method for determining the coefficients of a reversed power series
ACM SIGSAM Bulletin, 1977The method developed by van Orstrand is applied to the calculation of coefficients of a reversed power series. A FORMAC program which performs this calculation and sample output is given.
David L. Hall, B. Craig Meyers
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Residual Power Series Method for Fractional Diffusion Equations
Fundamenta Informaticae, 2017In this article, improved residual power series method (RPSM) is effectively implemented to find the approximate analytical solution of a time fractional diffusion equations. The proposed method is an analytic technique based on the generalized Taylor’s series formula which construct an analytical solution in the form of a convergent series.
Amit Kumar, Sunil Kumar, Sheng-Ping Yan
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The Scope of the Power Series Method
Mathematics Magazine, 2013This note examines the application of the power series method to the solution of second order homogeneous linear ODEs, and shows that it works in a straightforward way only under restrictive condit...
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On the power series method for eigenvalue calculation
Physics Letters A, 1987Abstract The power series method is applied to the Schrodinger eigenvalue equation with unsymmetric potentials. The calculation of upper and lower bounds to the eigenvalues is discussed. The anharmonic potential x2+αx3+βx4 is considered as an illustrative example.
Francisco M. Fernández +1 more
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A matrix method for power series potentials
Journal of Physics A: Mathematical and General, 2000Summary: Several useful techniques are described for treating power series potentials. These include: a moving row matrix nested multiplication method for constructing the Hamiltonian matrix; a scaled folding algorithm to find the eigenvalues; and an energy shift method which gives expectation values and eigencolumn elements.
Killingbeck, J. P., Scott, T., Rath, B.
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1991
It takes a little time and a few basic examples to develop intuition. This is particularly true of the subject of partial differential equations which has an enormous variety of technique and phenomena within its confines. This section describes the simplest nontrivial partial differential equation $${u_t}(t,x) + c{u_x}(t,x) = 0,t,x \in \mathbb{R ...
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It takes a little time and a few basic examples to develop intuition. This is particularly true of the subject of partial differential equations which has an enormous variety of technique and phenomena within its confines. This section describes the simplest nontrivial partial differential equation $${u_t}(t,x) + c{u_x}(t,x) = 0,t,x \in \mathbb{R ...
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A TAUBERIAN THEOREM FOR DISCRETE POWER SERIES METHODS
Analysis, 2002Let \(\sum^\infty_{n=0} a_n\) be a series with partial sums \(s_n\) \((n= 0,1,\dots)\). Let \(p_k\geq 0\), \(p_0> 0\) and \(P_n= p_0+\cdots+ p_n\to\infty\) \((n\to\infty)\). Suppose that the series \[ p(x)= \sum^\infty_{k= 0} p_k x^k \] has the radius of convergence 1. Put \[ p_s(x)= {1\over p(x)} \sum^\infty_{k=0} p_k s_k x^k.
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Power series methods of summability for series of fuzzy numbers and related Tauberian Theorems
Soft Computing, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sefa Anil Sezer, Ibrahim Çanak
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Summability Methods Obtained by Substitution of Power Series
SIAM Journal on Mathematical Analysis, 1975The Euler summability method is obtained by substituting into the series $\sum a_n x^n $ the expression $x = f(y) = {y / {(1 - qy)}}$, thereby obtaining a series $\sum b_n y^n $. In this paper we consider more general expressions for $f(y)$, $f(y) = \sum f_i y_i $. A class of sequences naturally associated with such methods is given by $\sigma ^ * $: $\
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A time series ensemble method to predict wind power
2014 IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG), 2014Wind power prediction refers to an approximation of the probable production of wind turbines in the near future. We present a time series ensemble framework to predict wind power. Time series wind data is transformed using a number of complementary methods. Wind power is predicted on each transformed feature space.
Sumaira Tasnim +4 more
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