Difference Equations and Differential Equations
Section 4.4. Using the Fundamental Theorem. Difference Equations to Differential Equations
... Because of results like this, many of the definite integrals that are encountered in applications cannot be evaluated using the Fundamental Theorem of Integral Calculus; instead, they mu[r] ...
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Section 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations
... Hence the derivative of the sum of two functions is the sum of their derivatives. A similar argument would show that the derivative of the difference of two functions is the difference of their derivatives. ...
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General boundary value problems for pseudo differential equations and related difference equations
... Indeed, this condition is a non-vanishing determinant of a certain system of linear alge- braic equations. But it is true for smooth boundary only, because it may be locally straight- ened by diffeomorphism ...
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Section 3.7. Rolle s Theorem and the Mean Value Theorem. Difference Equations to Differential Equations
... The Mean Value Theorem, of which Rolle’s Theorem is a special case, says that if f is differentiable on an interval, then there is some point in that interval at which the instantaneous [r] ...
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New applications of the variational iteration method from differential equations to q fractional difference equations
... The variational iteration method (VIM) [–] has been one of the often used non- linear methods in initial boundary value problems of differential equations. In this study, the extension of the method into FQC is ...
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6 Systems Represented by Differential and Difference Equations
... An important class of linear, time-invariant systems consists of systems rep- resented by linear constant-coefficient differential equations in continuous time and linear [r] ...
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Finding Differential Transform Using Difference Equations
... Terms—differential-transform, difference-operators, ...called differential transforms. The differential transform (DTM) was introduced by Zhou [2] in a study of electrical circuits which have ...
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Some results of certain types of difference and differential equations
... Liu et al Advances in Difference Equations 2012, 2012 127 http //www advancesindifferenceequations com/content/2012/1/127 R ES EA RCH Open Access Some results of certain types of difference and differ[.] ...
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Partial Differential and Difference Equations
... In other words, given any partial differential equation, it can be approximated by many different difference equations; however, as cited above and as shown by ma[r] ...
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Applications of differential difference equations
... They considered several methods o f approximation and it is interesting to compare the results they obtained with the exact solution.. Substituting this equation in[r] ...
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Semi-periodic solutions of difference and differential equations
... differential equations, we still need to define the notion of uniform semi-periodicity and prove that the associated Nemystkii operators map the set of semi-periodic sequences into ...differential equations ...
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An operator method for telegraph partial differential and difference equations
... telegraph equations; Cauchy problem; Hilbert space; difference schemes; stability 1 Introduction Hyperbolic partial differential equations arise in many branches of science and engineer- ing, ...these ...
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Growth of the Entire or Meromorphic Solutions of Differential-Difference Equations
... general differential difference polyno- mials with some condition on power of ...a differential- difference polynomial of degree d and weight Γ defined ...
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Rational Recursion Operators for Integrable Differential–Difference Equations
... for difference and rational (pseudo–difference) operators with coefficients in a difference field F and study their ...of difference operators from a preHamiltonian ...integrable ...
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Darboux transformations and Recursion operators for differential--difference equations
... 1 Introduction The aim of this paper is to give a comprehensive account of multi-Hamiltonian structures, recursion op- erators and Darboux-Lax representations for a wide class of integrable di ff erential-di ff erence ...
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Growth of the solutions of some q difference differential equations
... 23. Heittokangas, J, Korhonen, R, Laine, I, Rieppo, J, Tohge, K: Complex difference equations of Malmquist type. Comput. Methods Funct. Theory 1(1), 27-39 (2001) 24. Laine, I: Nevanlinna Theory and Complex ...
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Entire solutions of certain class of differential difference equations
... 3 Main results Now, we shall derive the following result similar to that of Theorems A and B, for extended differential-difference equations. First, we will prove the following result. Theorem . Let q be a ...
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Differential Equations
... problem. Differential equations are used by scientists and social scientists in a wide variety of disciplines, such as physics, chemistry, medicine, agronomy, population biology, epidemi- ology, astronomy, ...
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Differential Equations
... dt = where P t ( ) is the population at time t . 3) The temperature of a body changes at a rate proportional to the positive difference between the temperature of the body and its immediate environment. This is ...
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Finite difference schemes for linear stochastic integro-differential equations
... Abstract We study the rate of convergence of an explicit and an implicit-explicit finite dif- ference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear ...
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