Sentence examples for provided to validate from inspiring English sources

Finally, numerical results are provided to validate our proposed scheme.

Illustrating example is provided to validate our results.

In addition, an example is provided to validate our result.

Some numerical examples are provided to validate the theoretical results.

Various numerical results are provided to validate the proposed formulation.

Accurate numerical results are provided to validate the proposed algorithm.

Various numerical experiments are provided to validate the new schemes.

Finally, numerical simulations are provided to validate the theoretical results.

A sensitivity analysis is provided to validate the model.

Numerical simulations are provided to validate the results.

Simulation results are provided to validate the proposed algorithm.