Finite-difference Approximation for the u (k )-Derivative with O(hM−k+1) Accuracy: An Analytical Expression
نویسندگان
چکیده
An approximation of function u(x) as a Taylor series expansion about a point x0 at M points xi , ∼i = 1, 2, . . . ,M is used where xi are arbitrary-spaced. This approximation is a linear system for the derivatives u with an arbitrary accuracy. An analytical expression for the inverse matrix A−1 where A = [Aik] = 1 k! (xi − x0) is found. A finite-difference approximation of derivatives u of a given function u(x) at point x0 is derived in terms of the values u(xi). © 2006Wiley Periodicals, Inc. NumerMethods Partial Differential Eq 22: 1070–1079, 2006
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