Sentence examples for methods of orders from inspiring English sources

For the time integration attention is confined to a number of explicit Runge-Kutta methods of orders two up to four.

Furthermore, numerical tests on simplified reacting flows demonstrate the expected convergence rates for MISDC methods of orders three, four, and five.

Numerical results show that the conservative nature of the methods allows a robust representation of discontinuities and sharp gradients; the results also demonstrate the expected convergence rates for the methods of orders three, four, and five for smooth problems.

end{aligned} (26d) Using approximations (26a - 26d 26a - 26dference methedifference15b) and (16a)-(16b) retain their orders, and hence we obtain difference methods of orders (O(k^{2}+h_{l}^{2})) and (O(k^{2}+k^{2}h_{l}+h_{l}^{3})), respectively, for the numerical solution of the quasi-linear equation (15a - 15b 15a - 15b

An explicit Runge Kutta method of order four and implicit Runge Kutta methods of order two are constructed.

This idea is extended to construct one-point iterative methods of order four.

The new variable-step method is based on two P-stable methods of order eight and ten.

By consistent, we refer to the classical consistency constraints of Adams Bashforth methods of order-two.

They observe that for methods with stage order at least p−1, and design order p, starting methods of order at least p are sufficient.

We give explicit method (up to order 5) as well as pairs of embedded Runge Kutta methods of order 5 and 4 designed using the FSAL properties.

These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p+1.