Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation (Advances in Applied Mathematics and Mechanics, 2018)
The solution of boundary value problems (BVP) for fourth orderdifferential equations by their reduction to BVP for second orderequations, with the aim to use the available efficient algorithmsfor the latter ones, attracts attention from many researchers. Inthis paper, using the technique developed by the authors in recentworks we construct iterative method for a problem with complicatedmixed boundary conditions for biharmonic equation which isoriginated from nanofluidic physics. The convergence rate of themethod is proved and some numerical experiments are performed fortesting its dependence on a parameter appearing in boundaryconditions and on the position of the point where a transmission ofboundary conditions occurs.