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- W2146876056 abstract "In this paper a new, highly accurate method called PH is presented for the numerical integration of partial differential equations. The method is applied for the solution of the one-dimensional diffusion equation. Upon integrating the equation within a subdomain of space and time using the prismoidal approximation, a three-point implicit scheme is obtained with a truncation error of order O(k4, h6), where k and h represent the time and space steps respectively. The method is stable under the condition s = αk/h2 ⩽ S(δ), where the function S(δ) increases as the parameter δ decreases from 1/12 to negative values. In practice the method behaves as unconditionally stable upon choosing an appropriate value for δ. A new formula is also adopted for the implementation of a Neumann boundary condition, introducing a truncation error of order O(h4). Numerical solutions are obtained incorporating Dirichlet and Neumann boundary conditions. The results prove that our method is far more accurate than any other-implicit or explicit method." @default.
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- W2146876056 date "1994-02-15" @default.
- W2146876056 modified "2023-09-27" @default.
- W2146876056 title "New numerical method for partial differential equations. 1: Application to the diffusion equation" @default.
- W2146876056 cites W4300844655 @default.
- W2146876056 doi "https://doi.org/10.1002/fld.1650180303" @default.
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