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    Bonito, Andrea Lei, Wenyu and Pasciak, Joseph E. 2017. The approximation of parabolic equations involving fractional powers of elliptic operators. Journal of Computational and Applied Mathematics, Vol. 315, Issue. , p. 32.
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ITERATIVE SOLUTION OF SHIFTED POSITIVE-DEFINITE LINEAR SYSTEMS ARISING IN A NUMERICAL METHOD FOR THE HEAT EQUATION BASED ON LAPLACE TRANSFORMATION AND QUADRATURE

  • WILLIAM MCLEAN (a1) and VIDAR THOMÉE (a2)
Abstract

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive-definite matrix with a complex shift. We study iterative methods for such systems, considering the basic and preconditioned versions of first the Richardson algorithm and then a conjugate gradient method.

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      ITERATIVE SOLUTION OF SHIFTED POSITIVE-DEFINITE LINEAR SYSTEMS ARISING IN A NUMERICAL METHOD FOR THE HEAT EQUATION BASED ON LAPLACE TRANSFORMATION AND QUADRATURE
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      ITERATIVE SOLUTION OF SHIFTED POSITIVE-DEFINITE LINEAR SYSTEMS ARISING IN A NUMERICAL METHOD FOR THE HEAT EQUATION BASED ON LAPLACE TRANSFORMATION AND QUADRATURE
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      ITERATIVE SOLUTION OF SHIFTED POSITIVE-DEFINITE LINEAR SYSTEMS ARISING IN A NUMERICAL METHOD FOR THE HEAT EQUATION BASED ON LAPLACE TRANSFORMATION AND QUADRATURE
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Copyright
COPYRIGHT: © Australian Mathematical Society 2012
Corresponding author
✉For correspondence; e-mail: w.mclean@unsw.edu.au
References
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