We can then
approximate C([x.sub.i], [y.sub.j], [t.sub.n]) by [C.sup.n.sub.i,j] the value of the difference approximation of C(x, y, t) at point the grid point ([x.sub.i], [y.sub.j], [t.sub.n]) is defined by [x.sub.i] = i[DELTA]x for all i = 0, 1, 2, ..., L, = j[DELTA]y for all j = 0, 1, 2, ..., M, and [t.sub.n] = n[DELTA]t for all n = 0, 1, 2, ..., T, in which L, M, and T are positive integers.
The operator (5) satisfying (7) is called an infinitesimal
approximate symmetry or an
approximate operator admitted by (3).
Compared to
approximate methods, one would expect the exact analytical solution of the one-dimensional hindered diffusion model to yield more accurate characterization of the moisture absorption behavior.
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In the subsequent subsections we illustrate implementation of the above procedure, and we provide simulation results and
approximate similarity solutions for different cases of values of parameter [p.sub.1].
We remark that the choice of the
approximate solution (12) is not unique.
The generalized Filon methods we consider for (1.2)
approximate the integral with the exact integral of the approximating problem (1.4).
* A Prediction-based Energy-conserving
Approximate StoragE (P-EASE) is brought up, which improves the trade-off between the query precision and the energy conserving by using prediction method to return the
approximate querying result dynamically to cut down the location error.
In this paper we will use a new method to solve a problem of the type (1,2) and apply this method to find
approximate solutions for a problem with applications in economy.
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* $594 million:
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