Abstract
This chapter discusses L0-stable methods for constant coefficient parabolic equations. In recent years, a number of authors have concerned themselves with developing A0-stable and L0-stable methods for the numerical solution of second-order parabolic partial differential equations with constant coefficients. The procedure followed was the one (sometimes referred to as method of lines) in which the space derivative is approximated by a suitable finite difference replacement and the numerical solution is obtained by solving the resulting system of first-order ordinary differential equations. This approach was used in a study for first-order hyperbolic equations, for the fourth-order parabolic equations, and by Twizell for the second-order hyperbolic equations.
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