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IMA Journal of Numerical Analysis 1997 17(4):563-576; doi:10.1093/imanum/17.4.563
© 1997 by Institute of Mathematics and its Applications
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On the stability and convergence of discretizations of initial value p.d.e.s

M. B. GILES

Oxford University Computing Laboratory, Numerical Analysis Group Wolfson Building, Parks Road Oxford OX1 3QD, UK

This paper examines the stability and convergence of discretizations of initial value p.d.e.s using spatial discretization followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding sufficient conditions for both algebraic and strong stability. Sufficient conditions are also derived for convergence on a finite time interval.


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