Titlebook: Differential and Difference Equations; A Comparison of Meth Leonard C. Maximon Book 2016 Springer International Publishing Switzerland 2016

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,Green’s Function, point of the interval, we consider the equation in which the inhomogeneous term is the Dirac delta function, ., which is zero except at the point . within the interval. Its solution is called the Green’s function .. In considering the Green’s function for difference equations we follow closely the analysis presented for differential equations.

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Book 2016ifferential and difference equations.A comprehensive, detailed treatment of Green’s functions and the associatedinitial and boundary conditions is presented for differential and differenceequations of both arbitrary and second order. A dictionary of differenceequations with polynomial coefficients p

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Operators,rresponding operator, ., for difference equations and derive expressions for . operating on the product or the ratio of two functions and compare them to the corresponding expressions for the derivative operator.

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,Second Order Homogeneous and?Inhomogeneous Equations, Sect.?., if one solution of the homogeneous equation is known then the method of reduction of order transforms a second order equation into a first order equation, which can then be solved in closed form. If the original second order equation is homogeneous then the transformed first order equation

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Self-adjoint Linear Equations,ference, apply to operators and equations of all orders. However, given the fundamental place of second order equations, both differential and difference, for problems in classical and quantum physics, we restrict ourselves here to equations of second order, noting that most of the classical functio

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,Green’s Function,equation. In the method considered here, rather than determining the solution to the differential equation with the inhomogeneous term defined at each point of the interval, we consider the equation in which the inhomogeneous term is the Dirac delta function, ., which is zero except at the point . w

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