Abstract
1.1 Shift operator E ”Eyn = yn+1”is a linear operator, that is one of the most important tools in Numerical Analysis, used in Interpolations and Numerical solution of ODE and PDE. This operator is used as fundamental element in the structure of Difference equations. The Difference equations appear in Numerical solution of ordinary differential equations, Partial differential equation, Integral equations, Integrodifferential equation,[1], [2], [3], [4], [5]. Nonlinear difference equation (Euler method, Euler Modified method, Midpoint method,) appears mostly in numerical solution of initial value problem
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