Wavelet methods for solving three-dimensional partial differential equations

Abstract

We present, a collocation method based on Haar wavelet and Kronecker tensor product for solving three-dimensional partial differential equations. The method is based on approximating a sixth-order mixed derivative by a series of Haar wavelet basis functions. The present method is suitable for numerical solution of all kinds of three-dimensional Poisson and Helmholtz equations. Numerical examples are solving to establish the efficiency and accuracy of the present method. Numerical results obtained are better as compared to numerical results obtained in past.