Sentence examples for expand this solution from inspiring English sources

In order to find the solution of equation (1), we expand this solution into Taylor series with respect to t as follows: u ( x, t ) = ∑ n = 0 ∞ e x t n n !. Based on (4), the solution of equation (1) can be written in the following form: u ( x, t ) = e x + e x t α Γ ( α + 1 ) + e x t 2 α Γ ( 2 α + 1 ) + e x t 3 α Γ ( 3 α + 1 ) + ⋯. (5).

In order to find the solution of equation (6), we expand this solution into Taylor series with respect to x as follows: u ( x, t ) = ∑ n = 0 ∞ e t x n n !. Based on (9), the solution of equation (6) can be written in the following form: u ( x, t ) = e t + e t x α Γ ( α + 1 ) + e t x 2 α Γ ( 2 α + 1 ) + e t x 3 α Γ ( 3 α + 1 ) + ⋯. (10).

We have expanded this solution to describe the flow to a well with regularly spaced arrays of equidistant perforations along the wellbore wall.

He also writes that Google plans to expand this list with new solutions over time.

This means that we can expand the solution as ψ ( x ) = ∑ i = 1 2 ∑ m = 0 ∞ A m, i g i mπx L, Open image in new window (4).

We then develop a simple construction heuristic to expand the solution of the tree design problem by adding road segments.

We expand the solution function in a finite series in terms of composite translated sinc functions and some unknown coefficients.

Crossover operator Crossover operator plays an important role in GA since it helps to expand the solution space and get the global optimal.

Following the homotopy perturbation method [47], we expand the solution in terms of the homotopy parameter κ as u=u_{0}+kappa u_{1}+kappa ^{2}u_{2}+kappa ^{3}u_{3}+cdots.

This method uses an accelerated gradient descent solver and expands the solution to the wave equation as a series of the gradient solver updates.

The method is based on expanding the solution by Chebyshev wavelets with unknown coefficients.