Sentence examples for solution of this boundary from inspiring English sources

Several methods have been proposed for the numerical solution of this boundary value problem.

Several approaches for the numerical solution of this boundary value problem which have been considered in the literature, are reported.

According to Theorem 1, the uniformly valid zero-order asymptotic solution of this boundary value problem is given by y a s y ( x, ε ) = - x + 1 + M 1 e - 1 - x ε 1 - M 1 e - 1 - x ε - 1 + M 2 e x - 1 ε 1 - M 2 e x - 1 ε, (41). in which, M1 and M2 are, respectively, determined by 2 = 1 + M 1 1 - M 1, and - 2 = - 1 + M 2 1 - M 2. Consequently, M 1 = M 2 = 1 3 (42).

We use the Krasnosel'skiĭ fixed point theorem to obtain the sufficient conditions of the existence of two positive solutions for this boundary value problem of Caputo fractional difference equations depending on parameters.

For the latter case, one can show the global existence of unique strong solution of this initial boundary value problem in a similar way as that in [3, 9, 14].

This lemma is used to define the solution of the boundary value problem (1.5)–(1.5).

is a solution of the boundary value problem (II).

A dislocation based method is used to find the solution of the boundary value problem.

A differential turbulence model is used with numerical solution of the boundary layer equations.

Similarly, let be a weak solution of the boundary value problem (2.13).

Let (x t)) be a positive solution of the boundary value problem (1.10 - 1.11) in ((a, b)).