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Comparing time integrators for parabolic equations in two space dimensions with a mixed derivative

P.J. van der Houwen, B.P. Sommeijer, J.G. Verwer
1979 Journal of Computational and Applied Mathematics  
A numerical comparison is made between three integration methods for semi-discrete parabolic partial differential equations in two space variables with a mixed derivative.  ...  As pointed out by Gourlay & McKee [3], the choice of the second order line hopscotch method is, within the class of one-step splitting methods, selfevident.  ...  From the foregoing it shall be clear that a sensible choice of an integration method for semi-discrete parabolic equations is difficult.  ... 
doi:10.1016/0771-050x(79)90001-9 fatcat:awuegvbatrdolhq4dzzzoy6qzy

Contractivity of locally one-dimensional splitting methods

J. G. Verwer
1984 Numerische Mathematik  
The aim of this paper is to study contractivity properties of two locally one-dimensional splitting methods for non-linear, multi-space dimensional parabolic partial differential equations.  ...  for a large class of non-linear parabolic problems without restrictions on the size of the time step.  ...  Dekker for his careful reading of the manuscript.  ... 
doi:10.1007/bf01410109 fatcat:q7o3hjeu2fftldbo4fxibsa524

Splitting schemes for the semi-linear wave equation with dynamic boundary conditions [article]

Robert Altmann
2021 arXiv   pre-print
This paper introduces novel splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type.  ...  For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system.  ...  Here, we observe convergence rates of order one for Lie and order two for Strang splitting. 4.1. Semi-discrete system and bulk–surface splitting.  ... 
arXiv:2112.04321v1 fatcat:7ikz6snyxzhnhnhk5l54lgfkre

A Splitting Approach for Freezing Waves [chapter]

Robin Flohr, Jens Rottmann-Matthes
2018 Theory, Numerics and Applications of Hyperbolic Problems I  
equation (PDAE) and calculates a suitable co-moving frame on the fly.  ...  The benefit of splitting methods in this context lies in the possibility to solve hyperbolic and parabolic parts with different numerical algorithms.  ...  For this we use a method of lines (MOL) approach for (B): We choose a finite interval [L − , L + ] and choose a spatial grid with uniform step size ∆ x and spatially discretize with the semi-discrete version  ... 
doi:10.1007/978-3-319-91545-6_41 fatcat:wtg3xmzfwjf25a2gnmc3tk2qdy

A splitting approach for freezing waves [article]

Robin Flohr, Jens Rottmann-Matthes
2016 arXiv   pre-print
The benefit of splitting methods in this context lies in the possibility to solve hyperbolic and parabolic parts with different numerical algorithms.  ...  equation (PDE) into a partial differential algebraic equation (PDAE) and calculates a suitable co-moving frame on the fly.  ...  For this we use a method of lines (MOL) approach for (B): We choose a finite interval [L − , L + ] and choose a spatial grid with uniform step size ∆ x and spatially discretize with the semi-discrete version  ... 
arXiv:1611.10311v1 fatcat:74z5ydjl7rgwfefijm4xhjgrvq

Page 4371 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
Multiplicative Schwarz algorithms are proposed and analyzed for semi-discrete and fully discrete schemes based on time stepping along characteristics for solving convection diffusion equations.  ...  The paper describes a method for solving a parabolic equation backwards in time, where the elliptic operator is non-selfadjoint with coefficients that depend on the space variables.  ... 

Page 3418 of Mathematical Reviews Vol. , Issue 89F [page]

1989 Mathematical Reviews  
The Peaceman-Rachford type scheme (two-step splitting) is compared to a proposed three-step splitting method.  ...  In this paper the authors consider a conservative but dispersive finite difference method for (1), written in semi-discrete form as d at) qi ve + Uk (Sa!  ... 

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

F. Talay Akyildiz, K. Vajravelu
2018 Applied Mathematics and Nonlinear Sciences  
In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations.  ...  Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement  ...  In the literature, semi-implicit time stepping methods [12, 13] are commonly used to solve time dependent NPB equation (34) so that a large time step could be used for a stable simulation.  ... 
doi:10.21042/amns.2018.1.00019 fatcat:3bpm4bwomfgpvj3fpswucf7k34

Page 8472 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
parabolic equations at each time step by a Galerkin method in only one space direction.  ...  In this paper, the author derives optimal order error estimates for semi-discrete and fully discrete numerical solutions of initial- boundary value problems of pseudo-parabolic integro-differential equations  ... 

Page 7441 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
, LA) A posteriori error estimation with finite element semi- and fully discrete methods for nonlinear parabolic equations in one space dimension.  ...  Summary: “A posteriori error estimates for semi- and fully discrete finite element methods using a pth degree polynomial basis are con- sidered for nonlinear parabolic equations.  ... 

Page 5003 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Alternating direction, one time level semi-implicit and fully implicit splitting methods are discussed for 2D and 3D hydrostatic flows.  ...  Summary: “In this paper various semi-implicit discretization meth- ods for the equations of large scale free surface flows are outlined.  ... 

On Numerical Problems Caused by Discontinuities in Controls [chapter]

Christian Großmann, Antje Noack, Reiner Vanselow
2003 IFIP Advances in Information and Communication Technology  
In the present study effects to numerical methods for solving the state equations are illustrated.  ...  Moreover, an appropriate splitting of the solution is used to improve the numerical behavior of the discretization technique as weil as of the optimization method applied to the control problern itself  ...  In case of semi-discretization superposition is used for the solution of state as well as for the adjoint state equations.  ... 
doi:10.1007/978-0-387-35699-0_14 fatcat:mgeucde3unc75cvvmnq2t3ypxm

Page 2070 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Our estimates are applied to also show stability for time stepping methods.” 2002¢:65152 65M12 65B05 65J15 Descombes, Stéphane (F-ENSLY-PM; Lyon Convergence of a splitting method of high order for reaction-diffusion  ...  Summary: “In an attempt to show maximum-norm stability and smoothing estimates for finite element discretizations of parabolic problems on nonquasi-uniform triangulations, we consider the lumped mass method  ... 

Page 6029 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
error estimates for a semi-discrete finite element scheme.  ...  Both a semi-discrete scheme and a second-order implicit-time discretization method are discussed, and it is shown that the results are valid for all ¢ > 0.” 2002h:65156 65M60 65M12 Picasso, Marco (CH-LSNP  ... 

Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations [article]

Buyang Li, Weiwei Sun
2013 arXiv   pre-print
The method used in this paper can be applied to more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations for which previous works often require certain restriction  ...  Theoretical analysis is based on a new splitting of the error and precise analysis of a corresponding time-discrete system.  ...  Error bounds of the Galerkin finite element methods for the time-discrete parabolic equations in certain norm is dependent only upon the spatial mesh size h and independent of the time-step size τ .  ... 
arXiv:1208.4698v6 fatcat:my4eugksizhorkl6kyev7fgtse
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