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Traditionally, these methods were solved via Gaussian elimination, which requires computational work of O N3) per time step and O N2) of memory to store where N is the number of spatial grid points in the discretization.
Traditionally, these methods were solved via Gaussian type direct solvers, which requires O N3) of computational work per time step and O N2) of memory to store where N is the number of spatial grid points in the discretization.
Traditionally, these methods were solved with Gaussian elimination, which requires computational work of O N3) per time step and O N2) of memory to store where N is the number of spatial grid points in the discretization.
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Also, the main drawbacks of the earlier clustering-based methods are solved in this paper.
In the meantime, the correction equations in F-JDGSVD and G-JDGSVD methods are solved inexactly for large sparse problems, so we have linear convergence.
Three problems from ultrafiltration process design and analysis, typically solved using numerical methods, are solved analytically with the aid of the Exponential Integral special function.
Disadvantage of both mentioned methods is solving many differential equations of the second order or complicated symbolic calculations of so-called Adomian polynomials.
The design sensitivity equation of the direct differentiation method is solved at each time step without iteration.
The generalised eigenvalue problem obtained after discretization using the mixed finite element method is solved using the package LANSO.
The second method is solving a Poisson equation for the pressure field [23].
One advantage of this method is solving linear or nonlinear Volterra integral equation of the second kind with piecewise functions.
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