Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions

Numerical Algorithms ◽

10.1007/s11075-016-0206-8 ◽

2016 ◽

Vol 75 (1) ◽

pp. 261-283 ◽

Author(s):

Winfried Auzinger ◽

Othmar Koch ◽

Michael Quell

Keyword(s):

Boundary Conditions ◽

Periodic Boundary ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Periodic Boundary Conditions ◽

Splitting Methods ◽

Nonlinear Evolution Equations

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A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS

Journal of Applied Analysis & Computation ◽

10.11948/20180150 ◽

2020 ◽

Vol 10 (2) ◽

pp. 474-485

Author(s):

Huiqin Zhang ◽

◽

Yan Mo ◽

Zhibo Wang

Keyword(s):

Boundary Conditions ◽

Difference Method ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Variable Coefficients ◽

Diffusion Equations ◽

Order Difference

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Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations

Computer Physics Communications ◽

10.1016/j.cpc.2018.08.003 ◽

2019 ◽

Vol 234 ◽

pp. 55-71 ◽

Author(s):

Winfried Auzinger ◽

Iva Březinová ◽

Harald Hofstätter ◽

Othmar Koch ◽

Michael Quell

Keyword(s):

Wave Equations ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Splitting Methods ◽

Nonlinear Evolution Equations ◽

Local Error ◽

Local Error Estimation ◽

Adaptive Integration ◽

Selection Strategies ◽

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Existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions and its applications

10.21136/am.2018.0233-17 ◽

2018 ◽

Vol 63 (4) ◽

pp. 423-437 ◽

Author(s):

Sahbi Boussandel

Keyword(s):

Boundary Conditions ◽

Hilbert Spaces ◽

Periodic Boundary ◽

Evolution Equations ◽

Existence Of Solutions ◽

Periodic Boundary Conditions

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Superconvergence of high order FEMs for eigenvalue problems with periodic boundary conditions

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2009.02.038 ◽

2009 ◽

Vol 198 (30-32) ◽

pp. 2246-2259 ◽

Author(s):

H.-T. Huang ◽

S.-L. Chang ◽

C.-S. Chien ◽

Z.-C. Li

Keyword(s):

Boundary Conditions ◽

Periodic Boundary ◽

Eigenvalue Problems ◽

Periodic Boundary Conditions ◽

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Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

BIT Numerical Mathematics ◽

10.1007/s10543-016-0626-9 ◽

2016 ◽

Vol 57 (1) ◽

pp. 55-74 ◽

Author(s):

Winfried Auzinger ◽

Harald Hofstätter ◽

David Ketcheson ◽

Othmar Koch

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Splitting Methods ◽

Nonlinear Evolution Equations ◽

Adaptive Integration

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Frobenius integrable decompositions for high-order nonlinear evolution equations

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2010.10.024 ◽

2011 ◽

Vol 16 (8) ◽

pp. 3005-3010

Author(s):

Hongwei Yang ◽

Baoshu Yin ◽

Huanhe Dong

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations

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Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.09.027 ◽

2011 ◽

Vol 218 (7) ◽

pp. 3965-3972 ◽

Author(s):

Pavel N. Ryabov ◽

Dmitry I. Sinelshchikov ◽

Mark B. Kochanov

Keyword(s):

Exact Solutions ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Kudryashov Method

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Comparison theorems for nonlinear evolution equations and their application to the investigation of the dependence of the solutions of the equation ut=??(u) ON ? and on the boundary conditions

Journal of Soviet Mathematics ◽

10.1007/bf01104876 ◽

1986 ◽

Vol 35 (1) ◽

pp. 2282-2292

Author(s):

M. I. Khazan

Keyword(s):

Boundary Conditions ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Comparison Theorems

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Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier--Stokes Equations with Periodic Boundary Conditions

SIAM Journal on Numerical Analysis ◽

10.1137/21m1404144 ◽

2021 ◽

Vol 59 (6) ◽

pp. 2926-2954

Author(s):

Fukeng Huang ◽

Jie Shen

Keyword(s):

Error Analysis ◽

Boundary Conditions ◽

Periodic Boundary ◽

Stokes Equations ◽

Periodic Boundary Conditions ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Imex Schemes ◽

Stability And Error Analysis

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Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2012.09.002 ◽

2013 ◽

Vol 63 ◽

pp. 14-24 ◽

Author(s):

O. Koch ◽

Ch. Neuhauser ◽

M. Thalhammer

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Operator Splitting ◽

Time Integration ◽

Splitting Methods ◽

Nonlinear Evolution Equations ◽

Operator Splitting Methods ◽

Exponential Operator

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