| Abstract: |
| This paper presents a new accurate elliptic partial differential equation solver (AEPDES). The AEPDES has its nodes within the eight-step interval and targets elliptic partial differential equations on the two-dimensional domain. A collocation approach is adopted to develop this method, while a Hermite polynomial is employed as the basis function. The interpolation points are carefully selected at the two desired points, and at all the suitably preferred grid and off-grid points. By uniting the resulting equations and evaluating them at selected points,, the classical AEPDES is obtained. Investigating the numerical properties of the AEPDES, it was confirmed that the AEPDES is zero-stable and consistent. The accuracy and efficiency of the AEPDES were established by solving varying elliptic partial differential equations |
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