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BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 3/2015

01-09-2015

Monotone iterative ADI method for semilinear parabolic problems

Author: Igor Boglaev

Published in: BIT Numerical Mathematics | Issue 3/2015

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Abstract

The paper deals with numerical solving semilinear parabolic problems based on a nonlinear alternating direction implicit (ADI) scheme. The convergence of the nonlinear ADI scheme to the continuous solution is proved. The existence and uniqueness of a solution of the nonlinear ADI scheme are established. A monotone iterative ADI method is constructed. An analysis of convergence of the monotone iterative ADI method to the solution of the nonlinear ADI scheme on the whole time interval is given. Numerical experiments are presented.
previous article Spline element method for Monge–Ampère equations
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Literature
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Barrett, R., Berry, M., et al.: Templates for the Solution of Linear Systems. SIAM, Philadelphia (1994)
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Boglaev, I.: Monotone iterates with quadratic convergence rate for solving weighted average approximations to semilinear parabolic problems. Appl. Math. Comput. 217, 6390–6400 (2011)MATHMathSciNetCrossRef
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Pao, C.V.: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York (1992)MATH
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Pao, C.V.: Accelerated monotone iterative methods for finite difference equations of reaction-diffusion. Numer. Math. 79, 261–281 (1998)MATHMathSciNetCrossRef
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Wang, Y.-M., Lan, X.-L.: Higher-order monotone iterative methods for finite difference systems of nonlinear reaction-diffusion-convection equations. Appl. Numer. Math. 59, 2677–2693 (2009)MATHMathSciNetCrossRef
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Wang, Y.-M., Wang, J.: A higher-order compact ADI method with monotone iterative procedure for systems of reaction-diffusion equations. Comput. Math. Appl. 62, 2434–2451 (2011)MATHMathSciNetCrossRef
Metadata
Title
Monotone iterative ADI method for semilinear parabolic problems
Author
Igor Boglaev
Publication date
01-09-2015
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 3/2015
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-014-0529-6

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