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Unconditional stability of parallel difference schemes with second order accuracy for parabolic equation. (English) Zbl 1121.65096

Two kinds of difference schemes with intrinsic parallelism for the problem
\[ V_t=V_{xx},\;(x,t) \in (0; 1)\times (0; T],\quad V(0,t)=V(1,t)=0,\;t \in (0; T],\;V(x; 0)=V_0(x),\;x \in (0;1) \]
is constructed. The unconditional stability of these schemes is proved, and the convergence rate \(O(\tau + h^2)\) is obtained, where \(\tau\) is the step size in time and \(h\) in space. These results are extended to two dimensional space. Numerical examples that verify the theoretical results are given.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65Y05 Parallel numerical computation
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References:

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