Taylor's Method for solving O.D.E.'s
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چکیده
The Taylor series method is of general applicability and it is the standard to which we can compare the accuracy of the various other numerical methods for solving an I. V. P. It can be devised to have any specified degree of accuracy. Theorem (Taylor Series Method of Order n) Assume that f(t,y) is continuous and satisfies a Lipschits condition in the variable y, and consider the I. V. P. (initial value problem) with , over the interval . The Taylor series method uses the formulas , and
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