Sentence examples for inhomogeneous problem from inspiring English sources

(6.1) can be formulated by the inhomogeneous problem (1.1), where.

As a consequence, a scheme is stable for the inhomogeneous problem if it is stable for the homogeneous one.

Then, by suggesting own approaches, we construct the Green's function for the BVTP under consideration and find the resolvent function for the corresponding inhomogeneous problem.

By Duhamel's principle [27], it follows that the solution to an inhomogeneous problem is the superposition of the solutions to homogeneous problems.

Hence, mu I-A is sectorial of type omega=-mu< 0. Equation (17) can be formulated by the inhomogeneous problem (1), where u(t)=u t, cdot).

We treat the inhomogeneous problem and extend it to the setting of manifolds results obtained for the constant-coefficient Laplace operator on a Lipschitz domain in Euclidean space, with the Dirichlet boundary condition, by D. Jerison and C. Kenig.

Setting flux boundaries leads to more complicated inhomogeneous problems.

Multi-dimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing non-uniform grids.

The method is validated by comparing its predictions with DSMC solutions for spatially homogeneous and inhomogeneous problems.

Finally we investigate numerically the feasibility of the UWVF for both homogeneous and inhomogeneous problems and show examples of p- and h-convergence.

In spatially-inhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods.