Abstract
In this paper, the use of N-AGE and Newton-N-AGE iterative methods on a variable mesh for the solution of one dimensional parabolic initial boundary value problems is considered. Using three spatial grid points, a two level implicit formula based on Numerov type discretization is discussed. The local truncation error of the method is of \(O({k^2h_l^{-1} +kh_l +h_l^3})\), where h l > 0 and k > 0 are the step lengths in space and time directions, respectively. We use a special technique to handle singular parabolic equations. The advantage of using these algorithms is highlighted computationally.
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Mohanty, R.K. On the use of AGE algorithm with a high accuracy Numerov type variable mesh discretization for 1D non-linear parabolic equations. Numer Algor 54, 379–393 (2010). https://doi.org/10.1007/s11075-009-9341-9
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DOI: https://doi.org/10.1007/s11075-009-9341-9
Keywords
- Numerov type discretization
- Non-linear parabolic equation
- Non-uniform mesh
- N-AGE and Newton-N-AGE algorithms
- Burgers’ equation