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Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step.
For instance, the Split operator transforms.
Algebraic stability implies convergence of the real space split operator method for smooth absolutely integrable initial conditions.
In Section 3, the split operator method for the Dirac equation is presented, along with its exact correspondence with QW.
The methods used —second-order differencing, split operator propagation, Chebyshev polynomial expansion—are discussed in terms of their applicability to various classes of dynamic problems.
Consequently, the split operator method for the Klein Gordon equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition.
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In POS, we retain the FILTER, FOREACH and SPLIT operators since they have clear semantics in real-time circumstances.
Finite volume approach was attempted in this work with PISO (pressure implicit with split operators) algorithm for the pressure correction equations.
Finally, to design a time splitting operator strategy respecting both reactive two-phase flow physics and cost/accuracy ratio required for industrial computations.
Although non-conservative forms are used to derive numerical schemes for the two steps, the overall scheme resulting from this splitting operator strategy is conservative.
Split-operator approaches are methods in widespread use for numerical solutions of reaction/transport problems.
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