Sentence examples for representations for the solution from inspiring English sources

Novel integral representations for the solution of the Helmholtz and the modified Helmholtz equations formulated in the interior of a convex polygon are presented.

We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions.

Then we derive sampling representations for the solutions and Green's functions.

For diffusion equations of indefinite Sturm-Liouville type, we develop two equivalent methods of constructing explicit representations for the solutions.

This lemma will give a representation for the solution of (1), provided that the solution exists.

This lemma gives a representation for the solution of (1.1 - 1.2 1.1 - 1.2d that the solution exists.

So, formula (66) gives the representation for the solution of problem (3).

Now, let us obtain the representation for the solution of problem (2).

Let us first obtain the representation for the solution of problem (3).

Also, we derive a representation for the solution to (1.3) by converting the problem to an equivalent summation equation.

The method of quasilinearization is employed to provide an explicit analytic representation for the solution of nonlinear differential equations.