Numerical Solutions of the Elliptic Differential and the Planetary Motion Equations by Haar Wavelet - Quasilinearization Technique

Rawipa Yangchareonyuanyong, Sanoe Koonprasert, Sekson Sirisubtawee

Abstract

In this article, we apply the Haar-quasilinearization method (HQM) to solve the second order elliptic differential and planetary motion equations to which initial conditions and three types of boundary conditions including Dirichlet, Neumann-Robin, and Dirichlet-Neumann boundary conditions are equipped. By the HQM, both equations can be reduced to the recurrence relations which are linearized differential equations and then applied the Haar-quasilinearization method for solving these equations. Moreover, comparisons of the obtained results for the constructed problems with the exact solutions, HQM solutions, and some numerical solutions obtained using the standard methods are graphically demonstrated. In particular, the absolute errors, the L2-norm errors and the maximum absolute errors L∞ among these solutions are computed. As a result, the HQM is considered as the effective and rapidly convergent scheme.