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A series solution to the Thomas–Fermi equation
Applied Mathematics and Computation, 2008Abstract Nonlinear Thomas–Fermi equation is solved by an analytic technique named homotopy analysis method (HAM) in this paper. For a further improvement of the convergence and precision of the solution to Thomas–Fermi equation by HAM, different from previous work, however, a more generalized set of basis function and consequential auxiliary linear ...
Baoheng Yao
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Series Solution of Epidemic Model
2022The present paper is concerned with the approximate analytic series solution of the epidemic model. In place of the traditional numerical, perturbation or asymtotic methods, Laplace-Adomian decomposition method (LADM) is employed. To demonstrate the effort of the LADM an epidemic model, which has been worked on recently, has been solved.
Doğan, N., Akın, Ömer
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Series Solutions of Companding Problems
Bell System Technical Journal, 1983A formal power series solution (i) x(t) = Σ 1 ∞ mk x k (t) is given for the companding problem (ii) Bf{x(t)} = my(t), B{x(t)} = x(t), where B is the bandlimiting operator defined by Bg = (Bg)(t) = ∫ g(s)[sin λ(t − s)]/[π(t − s)]ds and f(t) has a Taylor series with f(0) = 0, f′(0) ≠ 0. Expressions for the x k are given in terms of the coefficients of f,
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2006
Abstract In this chapter, we investigate a special technique which provides solutions to a wide class of differential equations. Again, we concentrate on the homogeneous linear second-order equation where p 0, p 1, p 2 are continuous functions which we shall suppose throughout this chapter to have no common zeros.
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Abstract In this chapter, we investigate a special technique which provides solutions to a wide class of differential equations. Again, we concentrate on the homogeneous linear second-order equation where p 0, p 1, p 2 are continuous functions which we shall suppose throughout this chapter to have no common zeros.
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A series solution for the GVψ0 term of the Born series
Applied Mathematics and Computation, 1994A series representation for the function \(B(k, r):= \frac{i} {2k} \int_{-\infty}^\infty e^{ik|r- r'|} V(r') e^{ik r'} d r'\) is presented, where \(V\) arises as a potential in the differential equation (1) \((\frac{\partial^2} {\partial r^2}+ k^2)\psi (k, r)= V(r)\psi(k, r)\). The function \(B\) represents the second term of the Born series giving the
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2014
In Chap.6 it is shown how power series techniques can be used to represent the solution of scalar first- and second-order differential equations. Special attention is paid to Legendre’s equation, Bessel’s equation, and the hypergeometric equation since these equations often occur in the applications.
Martin Hermann, Masoud Saravi
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In Chap.6 it is shown how power series techniques can be used to represent the solution of scalar first- and second-order differential equations. Special attention is paid to Legendre’s equation, Bessel’s equation, and the hypergeometric equation since these equations often occur in the applications.
Martin Hermann, Masoud Saravi
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2019
Generally, second-order differential equations with variable coefficients cannot be solved in terms of the known functions. However, there is a fairly large class of differential equations whose solutions can be expressed either in terms of power series, or as simple combination of power series and elementary functions [1, 2, 3].
Ravi P. Agarwal +2 more
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Generally, second-order differential equations with variable coefficients cannot be solved in terms of the known functions. However, there is a fairly large class of differential equations whose solutions can be expressed either in terms of power series, or as simple combination of power series and elementary functions [1, 2, 3].
Ravi P. Agarwal +2 more
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Series solution to the Thomas–Fermi equation
Physics Letters A, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khan, Hina, Xu, Hang
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Power Series Solutions of ODEs and Frobenius Series
2001This chapter is devoted to the research of approximate solutions of nonlinear differential equations because for this kind of equation, it is exceptional to find the exact solutions. On the other hand, in the applications, it may be more useful to have an approximate solution with a simple form than an exact one with a very complex expression.
Addolorata Marasco, Antonio Romano
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