Sentence examples for advances the solution from inspiring English sources

The new algorithm advances the solution in the fluid domain with a standard upwind scheme and explicit time-stepping.

The semi-Lagrangian scheme advances the solution in time by integrating backward along flow trajectories, thus allowing large time steps while maintaining stability.

The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps.

The SL method advances the solutions of these PDEs in time by integrating backward along flow trajectories, thus allowing large time steps while maintaining stability.

To advance the solution one time step, one must solve a discrete system of nonlinear equations.

Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time.

The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size.

To advance the solution in time, we use a MUSCL-type scheme which couples a partial volume representation with a level set one to build the numerical fluxes.

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The numerical solution of a non-linear wave equation can be obtained by using spectral methods to resolve the unknown in space and the standard Crank-Nicolson differencing scheme to advance the solution in time.

Solutions are obtained by a Fourier spectral element method in conjunction with a semi-implicit method combining the second-order Adams-Bashforth and first-order backward Euler schemes for advancing the solution in time.