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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
DOI: https://doi.org/10.1090/S0025-5718-1970-0260215-1
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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0260215-1
Keywords: Stability, difference methods, mixed initial boundary-value problem, heat equation
Article copyright: © Copyright 1970 American Mathematical Society

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