Approximate solution of fractional integro-differential equations by Taylor expansion method
In this paper, Taylor expansion approach is presented for solving (approximately) a class of linear fractional integro-differential equations including those of Fredholm and of Volterra types.
Xian-Fang Li
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Quantum Functional Expansion to Solve Stochastic Differential Equations
2024 IEEE International Conference on Quantum Computing and Engineering (QCE)Jinhwan Sul, Jungin E. Kim, Yan Wang
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Some exact solutions for Toda type lattice differential equations using the improved (G′/G)‐expansion method [PDF]
Nonlinear lattice differential equations (also known as differential-difference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables.
Ismail Aslan
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Expansions of Differential Operators and Nonsmooth Solutions of Differential Equations
Cybernetics and Systems Analysis, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Asymptotic Expansions of Solutions of Differential Equations
Journal of Mathematical Physics, 1965A generalization of Ford's method, concerning the asymptotic expansions of solutions of differential equations with polynomial coefficients and with three or more regular singular points and one irregular at infinity, is presented. The analysis is subsequently extended to the special case of integral values for the difference of exponents of the ...
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Application of rational expansion method for stochastic differential equations
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MeiJiao Wang, Qi Wang
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On certain expansions of the solutions of Mathieu'S differential equation
Mathematical Proceedings of the Cambridge Philosophical Society, 19421. There are several known types of expansions of Mathieu functions, i.e. mod 2π periodic solutions of Mathieu's equation ((9), chap. 19),The simplest expansion is the Fourier seriesAlmost equally well known are Heine's expansion ((4), p.
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Taylor series expansion of delay differential equations—A warning
Journal of Theoretical Biology, 1974Abstract Attempts have been made to approximate the solutions of differential-difference equations using a Taylor series expansion of the lag term and ignoring high order derivatives. It is demonstrated that such a technique may lead to serious errors and that it is, perhaps, easier and certainly more valid to apply numerical methods directly.
A, Mazanov, K P, Tognetti
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Series Expansions of Solutions of Differential-Difference Parabolic Equations
Mathematical NoteszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muravnik, A. B. +2 more
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A cumulant expansion for stochastic linear differential equations. II
Physica, 1974Abstract A linear differential equation whose coefficients are stochastic functions, together with a fixed initial condition, defines a stochastic process. A systematic expansion is given for the expectation value of this process. The expansion parameter is the product of the magnitude of the fluctuations and their auto-correlation time.
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