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Generalized finite-difference schemes [PDF]
Mathematics of Computation, 1969 Finite-difference schemes for initial boundary-value problems for partial differential equations lead to systems of equations which must be solved at each time step. Other methods also lead to systems of equations. We call a method a generalized finite-difference scheme if the matrix of coefficients of the system is sparse.
Swartz, B., Wendroff, B.
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Numerical Analysis of Time-Accurate Solution of Nonlinear Flow Models by Implicit Finite Differences
Nonlinear Analysis, 2003 Implicit finite differences are often applied to solve flow models. A standard technique to solve these equations is Newton's method. lf time step is too large although the difference equation could be computationally stable, Newton's method may fail ...
S. K. Dey
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Mathematics, 2021 In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations.
M. Luísa Morgado +2 more
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A Nodal Immersed Finite Element-Finite Difference Method
SSRN Electronic Journal, 2022 The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. This method uses a finite element (FE) method to approximate the stresses and forces on a structural mesh and a finite difference (FD) method to approximate the momentum of the entire fluid ...
David R. Wells +3 more
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IEEE AccessGradient variance errors in gradient-based search methods are largely mitigated using momentum, however the bias gradient errors may fail the numerical search methods in reaching the true optimum.
Mircea-Bogdan Radac, Titus Nicolae
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Frictionless Motion of Diffuse Interfaces by Sharp Phase-Field Modeling
Crystals, 2022 Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits the overall ...
Michael Fleck +2 more
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Computation, 2022 Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line.
Vladimir G. Dmitriev +3 more
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Approximate Solutions of Time Fractional Diffusion Wave Models
Mathematics, 2019 In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations.
Abdul Ghafoor +4 more
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Numerical Study of Electro-Osmotic Fluid Flow and Vortex Formation
Micromachines, 2019 The phenomenon of electro-osmosis was studied by performing numerical simulations on the flow between parallel walls and at the nozzle microchannels.
Wesley De Souza Bezerra +2 more
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Finite Difference of Adjoint or Adjoint of Finite Difference? [PDF]
Monthly Weather Review, 1997 Abstract Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time tf, averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the
Sirkes, Ziv, Tziperman, Eli
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