A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obtained system of algebraic equations. The efficiency of the method is demonstrated by four numerical examples.