Sentence examples similar to multi dimensional cases from inspiring English sources

The methodology we propose in this investigation can be applied to multi-dimensional cases.

In the original THINC scheme, one-dimensional THINC scheme was straightforwardly used for multi-dimensional cases.

In this paper, only a one-dimensional case is considered for simplicity, and the multi-dimensional cases are dealt similarly.

Compact finite difference schemes are difficult to apply for multi-dimensional cases or for cylindrical and spherical coordinate cases.

Some remaining issues linked to the modeling of flame propagation in multi-dimensional cases are eventually discussed.

By using the ideas in this article we can obviously also prove some Hardy-type inequalities with more general weights and also in multi-dimensional cases.

Many numerical schemes have been proposed for some well-known one-dimensional equations, however, little numerical analysis has been published for the multi-dimensional cases.

For simplicity, we only consider one-dimensional Wiener process of white noise in this paper; it is straightforward but tedious to extend all perturbation results presented in this paper for multi-dimensional cases.

Moreover, its numerical integration in multi-dimensional cases, e.g., when using Monte Carlo sampling methods, is therefore computationally too expensive for realistic physical models, especially for those involving the solution of partial differential equations.

We consider both one dimensional and higher dimensional cases.

The higher dimensional cases are similar.