Now, the numeration system of
approximation of solution is investigated using manifold under proper parameter by parts of solution in lower frequency spaces according to the reduced system of (3).
In this section, we present an
approximation method, based on the expansion of a solution of a differential equation in a series in a small parameter.
where [DELTA][W.sup.(j).sub.k] = [W.sub.k]((j + 1)h) - [W.sub.k](jh) and our numerical
approximation to X(jh) will be denoted [x.sup.(j)].
In Section 4, we obtain weighted
approximation theorem, establish local
approximation theorems, estimate the rate of convergence, give a convergence theorem for the Lipschitz continuous functions, and also obtain a Voronovskaja-type asymptotic formula.
As we know from the trigonometric Fourier
approximation, the strong convergence of the Fourier partial sums is not guaranteed for all f [member of] X.
Precision Analysis of Different Approximating Methods In the inverse square root
approximation, errors ([E.sub.total]) can be caused by the approximated methods and the truncation processes in hardware implementation.
4, we similarly plot the relative error in the second-order
approximation for ice.
If a regular expansion can be constructed in [[OMEGA].sub.1], one can write down the
approximation as
In this section we obtain an
approximation formula to plain vanilla call price by approximating terms (I)-(IV).