Sentence examples for method of operators from inspiring English sources

The method of operators as a tool for investigation of the solution to hyperbolic equations in Hilbert and Banach spaces has been used extensively in [17] [29].

Then (sigma(mathbf{H})) = cup_{i=1}^{m}sigma(mathbf{H}_{i})), which is obtained by the direct sum decomposition method of operators (see [16]).

The method of operators as a tool for the investigation of the solution of local and nonlocal problems for partial differential equations in Hilbert and Banach spaces has been systematically developed by several authors (see, e.g., [1 27]).

The method of operators as a tool for investigation of the well-posedness of boundary value problems for parabolic partial differential equations is well known (see, e.g., [32 41]).

The method of operators as a tool for the investigation of the solution of local and nonlocal problems to hyperbolic differential equations in Hilbert and Banach spaces, has been systematically developed by several authors (see, e.g., [1 3, 10, 11]).

A common second-order accurate method for coupling operators is Strang's method of operator splitting.

Additionally, it is a provably stable algorithm as opposed to other boundary perturbation approaches such as Bruno and Reitich's "method of field expansions" or Milder's "method of operator expansions".

These variations can be computed in a number of ways, but we establish, via a variety of computational experiments, the superior effectiveness of our new approach as compared with another popular Boundary Perturbation algorithm (the method of Operator Expansions).

We apply the method of operator splitting on the generalized Korteweg--de Vries (KdV) equation ut+f u x+ϵuxxx=0, by solving the nonlinear conservation law ut+f u x=0 and the linear dispersive equation ut+ϵuxxx=0 sequentially.

This result was proved by direct sum decomposition methods of operators and estimation of the corresponding quadratic forms.

This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.