Sentence examples for an approximation solution for from inspiring English sources

In 2008, the author introduced the generalized nonlinear ordered variational inequalities (the ordered equations) and studied an approximation algorithm and an approximation solution for a class of generalized nonlinear ordered variational inequalities and ordered equations in ordered Banach spaces [20].

We will prove optimal structures in the problem and propose an optimal and an efficient approximation solution for this problem.

Therefore, we provide a theoretical approximation solution for this problem.

An approximation solution is introduced for the dynamic response of a two-layered cylindrical shell of circular cross-section subjected to an underwater explosive shock wave.

We also notice that for λ = 0 the present problem corresponds to the MHD boundary layer flow over a static wedge, which has been considered by Apelblat [24], in which the MHD wedge problem was solved using the Laplace transform method to give an infinite series approximation solution for f ″ ( 0 ) and g ″ ( 0 ).

end{aligned} (1.6 Fefferman searched for a solution (rho <0) on D such that (u=-log (-rho )) is strictly plurisubharmonic in D. He proved the uniqueness and gave a formal or approximation solution for (1.5).

In 2008 the author introduced and studied the approximation algorithm and the approximation solution for a class of generalized nonlinear ordered variational inequalities and ordered equations to find x ∈ X such that A ( g ( x ) ) ≥ θ ( A ( x ) and g ( x ) are single-valued mappings) in ordered Banach spaces [21].

And very recently, the author introduced and studied the approximation theory, the approximation algorithm and the approximation solution for generalized nonlinear ordered variational inequalities (ordered equations, inclusion problems) in ordered Hilbert spaces or ordered Banach spaces [21 25].

Very recently, the approximation solution for general nonlinear ordered variational inequalities and ordered equations [1, 2] and a nonlinear ordered inclusion problem [8, 9] have been studied by Li in an ordered Banach space.

Bickley [7], Albasiny and Hoskins [8, 9], and Fyfe [10] have demonstrated the use of cubic spline function for obtaining the second order approximation solution for two point boundary value problems.

Section 3 presents an approximation algorithm to obtain an ε-approximation solution for problem (P) which is FPTAS by its computational complexity.