Sentence examples for solutions error from inspiring English sources

To establish asymptotic stability we prove the stability estimates by using integral representations of the solutions via asymptotic solutions, error estimates, and calculus on time scales.

It can be seen that the present solution is in close agreement with those solutions (errors <0.2%).

This allows a reliable estimation of the solution error.

The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance.

Assessing solution error continues to be a formidable task when numerically solving practical flow problems.

It is shown that either way, solution error is second order in the mesh spacing.

The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively.

Significant accuracy gains in manufactured solution error norms are noted even with modest promotion of the underlying polynomial order.

The solution error is monitored and automatic refinement can continue until it is reduced to a satisfactory level.

Second, the error introduced by the domain decomposition is small relative to the solution error obtained in a single-grid calculation.

We then present an analysis of the method which confirms that the solution error does indeed reduce as the cell size is reduced.