Chebyshev tau meshless method based on the highest derivative for fourth order equations

It is well known that the numerical integration process is much less sensitive than numerical differential process when dealing with the differential equations. After integration, accuracy is no longer limited by that of the slowly convergent series for the highest derivative, but only by that of the unknown function itself. In this paper, a Chebyshev tau meshless method based on the highest derivative (CTMMHD) is developed for fourth order equations on irregularly shaped domains with complex boundary conditions. The problem domain is embedded in a domain of regular shape. The integration and multiplication of Chebyshev expansions are given in matrix representations. Several numerical experiments including standard biharmonic problems, problems with variable coefficients and nonlinear problems are implemented to verify the high accuracy and efficiency of our method.