'Modified euler' presentation slideshows

INITIAL VALUE PROBLEMS

INITIAL VALUE PROBLEMS. An approximation to this is:. for small values of h. REMEMBER NUMERICAL DIFFERENTIATION. The derivative of y (x) at x 0 is:. Forward Difference Formula. Provided h is small. The value of a function at. can be approximated if we know its value.

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Numerical Solution of Ordinary Differential Equation

Numerical Solution of Ordinary Differential Equation. A first order initial value problem of ODE may be written in the form Example: Numerical methods for ordinary differential equations calculate solution on the points, where h is the steps size . Numerical Methods for ODE. Euler Methods

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?????????? ???????? ???? (Euler) ??? ? ????? Order( h 2 ) ???? ( h 2 ?????? h ?????????? ) ?

?????????? ???????? ???? (Euler) ??? ? ????? Order( h 2 ) ???? ( h 2 ?????? h ?????????? ) ? F(x, y, h ) = h f(x, y) ???? y(x + h ) ? y(x) + ?(x, y, h ) y(x + h ) ? y(x) + F(x, y, h ) Y(x + h ) ? Y(x) + h f(x, y) ??????. ???? h 2 ?????? h ????????? ??????

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