Results 211 to 220 of about 88,452 (260)
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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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Celestial Mechanics, 1970
A means of extending the radius of convergence of a power series solution of a system of differential equations is presented. It is essentially a change of the independent variable by means of a conformal mapping. Conditions on this change of variables which should yield a computational advantage are discussed.
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A means of extending the radius of convergence of a power series solution of a system of differential equations is presented. It is essentially a change of the independent variable by means of a conformal mapping. Conditions on this change of variables which should yield a computational advantage are discussed.
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Series solutions to linear integral equations
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher S. Withers +1 more
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2016
In this chapter we describe the series solution method for generalized Volterra integral equations and generalized Volterra integro-differential equations.
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In this chapter we describe the series solution method for generalized Volterra integral equations and generalized Volterra integro-differential equations.
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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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2016
In this chapter, the Separation of Variables method is used to find a solution to the finite cable equation. The cable is subjected to an impulse of current at some location on the cable itself and the corresponding solution must be written as an infinite series in terms of what are called Fourier sin and cosine series.
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In this chapter, the Separation of Variables method is used to find a solution to the finite cable equation. The cable is subjected to an impulse of current at some location on the cable itself and the corresponding solution must be written as an infinite series in terms of what are called Fourier sin and cosine series.
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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 ...
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2015
We have already seen in 3 that the solution of differential equations of constants coefficient depends on the solutions of the associated algebraic characteristic equation. There is no similar procedure for solving linear differential equation with variable coefficients.
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We have already seen in 3 that the solution of differential equations of constants coefficient depends on the solutions of the associated algebraic characteristic equation. There is no similar procedure for solving linear differential equation with variable coefficients.
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