# On the WKBJ approximation

## Related Articles

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We show that differential[sup n, sub x](u[sup epsilon] - u) tends to zero (as epsilon arrow right 0) uniformly over (0,T] x R[sup d] in a weighted Holder-continuity norm or, in the unscaled case, that Differential[sup n, sub x][v[sup epsilon](tau, x) - u(epsilon tau, x)] converges to 0 uniformly...

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The problem of optimally approximating a function with a linear expansion over a redundant dictionary of waveforms is NP-hard. The greedy matching pursuit algorithm and its orthogonalized variant produce suboptimal function expansions by iteratively choosing dictionary waveforms that best match...

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For an ellipticoperator with rapidly oscillating coefficients we consider a homogenization procedure near the edge of an interior gap in the spectrum of this operator. At a point close to the edge, we obtain an approximation of the resolvent in the operator L2(â„)-norm. The first order...

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Usually the Stokes equations that govern a flow in a smooth thin domain (with thickness of order [variant_greek_epsilon]) are related to the Reynolds equation for the pressure psmooth. We begin by showing that the flow may be accelerated using adequate rugosity profiles on the bottom. Indeed, we...

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Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Algorithm to prove the stability and convergence of the approximations.

- An Approximation for the Zakai Equation. Hu, Y.; Kallianpur, G.; Xiong, J. // Applied Mathematics & Optimization;2002, Vol. 45 Issue 1, p23
In this article we consider a polygonal approximation to the unnormalized conditional measure of a filtering problem, which is the solution of the Zakai stochastic differential equation on measure space. An estimate of the convergence rate based on a distance which is equivalent to the weak...

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[p]Discretization methods for ordinary differential equations based on the use of matrix exponentials have been known for decades. This set of ideas has come off age and acquired greater interest recently, within the context of geometric integration[/em] and discretization methods on manifolds...

- On Asymptotic Orders of n-Term Approximations and Non-Linear n-Widths. Dinh Dung // Vietnam Journal of Mathematics;Dec99, Vol. 27 Issue 4, p363
Investigates the orders of n-term approximation. Advantages of non-linear approximation; Definitions of non-linear widths; Classes of multivariate functions.