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Set differential equations versus fuzzy differential equations
Applied Mathematics and Computation, 2005The paper is devoted to establish some results on existence, uniqueness and flow invariance for set differential equations, and their connection with fuzzy differential equations. Both types of differential equations are emergent research areas, so the background included in this paper will be appreciated for all people interested in the topic.
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Applied Mathematics and Computation, 2016
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Christopher S. Withers +1 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher S. Withers +1 more
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The Mathematical Gazette, 1945
1. We deal with the equation where ψ(ωt) is continuous, periodic in t with period 2π/ω a,
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1. We deal with the equation where ψ(ωt) is continuous, periodic in t with period 2π/ω a,
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On the Eigenvalues of Differential Equations
American Journal of Mathematics, 1951is the t-value satisfying q (t) S. The assumption of the existence of a third derivative, as pointed out by Milne, was unessential to his proof. Titchmarsh [5] gave a simplified proof of (4) retaining all of Milne's conditions, except that concerning the existence of a third derivative.
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Stochastic differential equations
Physics Reports, 1976Abstract In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ c , where α measures the size of the fluctuations and τ c their autocorrelation time. This
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geometry of differential equations
Journal of Soviet Mathematics, 1983This paper contains a survey of papers on the geometry of differential equations, which appeared no earlier than 1972, continuing the general survey (RZhMat, 1974, 11A800), and considers in more detail a special cycle of investigations of the geometry of systems of partial differential equations, distinguished by the presence of practical applications.
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Stochastic differential equations
2011In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.
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1966
Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Ordinary Differential Equations
2012In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
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