Abstract
For the numerical integration of the system of three dimensional mildly nonlinear biharmonic problems of second kind, we report two sets of difference methods of order two and four over a cubic domain. The second order derivatives of the solutions are obtained as by-product of the methods. We use 19 and 27 grid points for second and fourth order methods respectively and do not require fictitious points in order to approximate the boundary conditions. We compare the new second and fourth order formulas with the exact solutions both in singular and non-singular cases.
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