The paper considers the second-order nonlinear boundary value problem (NBVP), which is equipped with integral conditions (BCs). Two novel iterative algorithms are developed to overcome difficulty of NBVP double nonlinearities involved. In first algorithm, two nonlocal shape functions incorporating linear terms derived, and a function (NBSF) formulated assist solution. Let solution be NBSF so th...

The numerical treatment of boundary integral equations in the form of boundary element methods has became very popular and powerful tool for engineering computations of boundary value problems, in addition to finite difference and finite element methods. Here, we present some of the most important analytical and numerical aspects of the boundary integral equation. The concept of the principle s...

The development of separate building performance simulation tools has brought about a significant need for the integration of multi-domain simulations that would enable multiple building performance analyses to be conducted from a single building model. Insufficient data integration between the tools and Building Information Modeling (BIM) currently prevents the efficient production of comprehe...

we consider a mixed boundary value problem for a quarter-plane with a robin condition on one edge. we have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.