Results 131 to 140 of about 4,525,221 (172)
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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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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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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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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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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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Journal of Applied Mathematics and Computing, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Series Solutions for Structural Mobility
The Journal of the Acoustical Society of America, 1965In investigating the behavior of subcomponents of a structural system, attention is often given to the matching of mobility or impedance at mounting or junction points. Thus, if the mobility at a point in a certain frequency range is of interest, the structure supporting that point might be a black box containing a structural model designed to ...
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Series Solutions for Differential Equations
2019In more sophisticated courses in mathematical physics or “special functions,” a different type of linear differential equation frequently arises from those we have studied to date.
Allan Struthers, Merle Potter
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Branching solutions and Lie series
Celestial Mechanics & Dynamical Astronomy, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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