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Mathematics of Computation

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Maximum norm stability of difference approximations to the mixed initial boundary-value problem for the heat equation

Author: J. M. Varah
Journal: Math. Comp. 24 (1970), 31-44
MSC: Primary 65.68
MathSciNet review: 0260215
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Abstract: We consider the heat equation ${u_t} = {u_{xx}}$ in the quarter-plane $x \geqq 0$, $t \geqq 0$ with initial condition $u(x,0) = f(x)$ and boundary condition $\alpha u(0,t) + {u_x}(0,t) = 0$. We are concerned with the stability of difference approximations ${\upsilon _\nu }^{n + 1} = Q{\upsilon _\nu }^n$ to this problem. Using the resolvent operator ${(Q - zI)^{ - 1}}$, we give sufficient conditions for consistent, onestep explicit schemes to be stable in the maximum norm.

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Keywords: Stability, difference methods, mixed initial boundary-value problem, heat equation
Article copyright: © Copyright 1970 American Mathematical Society