Titlebook: Difference Equations from Differential Equations; Wilbert James Lick Book 1989 Springer-Verlag Berlin, Heidelberg 1989 Algebra.algorithm.a

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Parabolic Equations,ssified in much the same way as ordinary differential equations, e.g., first-order or higher-order, linear or nonlinear, homogeneous or non-homogeneous. Certain properties of PDEs are important in determining the appropriate numerical analysis for these PDEs and, because of this, those properties will be briefly reviewed here.

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Hyperbolic Equations,l be functions of x, y, ⌽, ∂⌽/∂x, and ∂ø/∂y. For b. − 4ac > 0, the equation is hyperbolic and two families of real characteristics exist. As mentioned previously, characteristics are lines across which derivatives of the dependent variables may be discontinuous and along which infinitesimal disturbances may propagate.

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Elliptic Equations,Elliptic partial differential equations usually describe the steady-state limit of problems where the time-dependent problem is described by parabolic or hyperbolic partial differential equations. They may also describe problems where the time dependence has an assumed form, such as sinusoidal with time.

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Difference Equations from Differential Equations978-3-642-83701-2Series ISSN 0176-5035

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E. Klieser,E. Lehmann,W. H. Straußc difference equations from ordinary differential equations. A secondary purpose is to develop the proper ideas and procedures for later use in deriving difference equations from partial differential equations.