Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

Journal of Mathematical Sciences ◽

10.1007/s10958-018-3673-8 ◽

2018 ◽

Vol 229 (3) ◽

pp. 227-240

Author(s):

A. P. Yankovskii

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Parabolic Type ◽

Initial Boundary ◽

Spectral Stability ◽

Explicit Methods ◽

Type I ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

Journal of Mathematical Sciences ◽

10.1007/s10958-018-4101-9 ◽

2018 ◽

Vol 236 (2) ◽

pp. 115-136

Author(s):

А. P. Yankovskii

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Parabolic Type ◽

Initial Boundary ◽

Spectral Stability ◽

Type Ii ◽

Initial Boundary Value Problems ◽

Implicit Methods ◽

Runge Kutta ◽

Initial Boundary Value

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Runge-Kutta methods without order reduction for linear initial boundary value problems

Numerische Mathematik ◽

10.1007/s002110100332 ◽

2002 ◽

Vol 91 (4) ◽

pp. 577-603 ◽

Author(s):

Isaías Alonso-Mallo

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Order Reduction ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Optimal orders of convergence for Runge–Kutta methods and linear, initial boundary value problems

Applied Numerical Mathematics ◽

10.1016/s0168-9274(02)00110-1 ◽

2003 ◽

Vol 44 (1-2) ◽

pp. 1-19 ◽

Author(s):

I. Alonso-Mallo ◽

C. Palencia

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems

Mathematics of Computation ◽

10.1090/s0025-5718-01-01362-x ◽

2001 ◽

Vol 71 (240) ◽

pp. 1529-1544 ◽

Author(s):

M. P. Calvo ◽

C. Palencia

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Order Reduction ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Galerkin-Runge-Kutta methods and hyperbolic initial boundary value problems

Computing ◽

10.1007/bf02248779 ◽

1977 ◽

Vol 18 (1) ◽

pp. 79-88 ◽

Author(s):

E. Gekeler

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Spectral-fractional step Runge--Kutta discretizations for initial boundary value problems with time dependent boundary conditions

Mathematics of Computation ◽

10.1090/s0025-5718-04-01660-6 ◽

2004 ◽

Vol 73 (248) ◽

pp. 1801-1826 ◽

Author(s):

I. Alonso-Mallo ◽

B. Cano ◽

J. C. Jorge

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Boundary Value ◽

Initial Boundary ◽

Time Dependent ◽

Fractional Step ◽

Initial Boundary Value Problems ◽

Runge Kutta ◽

Initial Boundary Value

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Preserving concavity in initial-boundary value problems of parabolic type and in its numerical solution

Periodica Mathematica Hungarica ◽

10.1007/bf01876627 ◽

1995 ◽

Vol 30 (2) ◽

pp. 135-139 ◽

Author(s):

I. Faragó ◽

T. Pfeil

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Boundary Value ◽

Parabolic Type ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Initial Boundary Value

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The asymptotic behavior of solutions of some nonlinear initial-boundary value problems of parabolic type

10.31274/rtd-180813-11956 ◽

1990 ◽

Author(s):

Keng Deng

Keyword(s):

Asymptotic Behavior ◽

Boundary Value Problems ◽

Boundary Value ◽

Parabolic Type ◽

Initial Boundary ◽

Asymptotic Behavior Of Solutions ◽

Initial Boundary Value Problems ◽

Initial Boundary Value

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Non-linear initial boundary value problems of hyperbolic-parabolic type. A general investigation of admissible couplings between systems of higher order. Part 3: applications

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.285 ◽

2002 ◽

Vol 25 (3) ◽

pp. 241-262 ◽

Author(s):

Stefan Ebenfeld

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Parabolic Type ◽

Type A ◽

Initial Boundary ◽

Higher Order ◽

Initial Boundary Value Problems ◽

General Investigation ◽

Initial Boundary Value

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The Correct Formulation of Intermediate Boundary Conditions for Runge--Kutta Time Integration of Initial Boundary Value Problems

SIAM Journal on Scientific Computing ◽

10.1137/s1064827594273948 ◽

1997 ◽

Vol 18 (5) ◽

pp. 1255-1266 ◽

Author(s):

D. Pathria

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Boundary Value ◽

Time Integration ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Correct Formulation ◽

Runge Kutta ◽

Initial Boundary Value

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