TY - JOUR
T1 - A New High Accuracy Off-Step Discretisation for the Solution of 2D Nonlinear Triharmonic Equations
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 228
EP - 246
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.140713.130813a
UR - https://global-sci.org/intro/article_detail/eajam/10856.html
KW - High accuracy finite differences, off-step discretisation, two-dimensional nonlinear triharmonic equations, Laplacian, biharmonic, triharmonic, maximum absolute errors.
AB - <p style="text-align: justify;">In this article, we derive a new fourth-order finite difference formula based
on off-step discretisation for the solution of two-dimensional nonlinear triharmonic partial
differential equations on a 9-point compact stencil, where the values of $u$, $(∂^{2}u/∂n^2)$ and $(∂^{4}u/∂n^{4})$ are prescribed on the boundary. We introduce new ways to handle the
boundary conditions, so there is no need to discretise the boundary conditions involving
the partial derivatives. The Laplacian and biharmonic of the solution are obtained as
a by-product of our approach, and we only need to solve a system of three equations.
The new method is directly applicable to singular problems, and we do not require any
fictitious points for computation. We compare its advantages and implementation with
existing basic iterative methods, and numerical examples are considered to verify its
fourth-order convergence rate.</p>