Numerical solution of linear and nonlinear elliptic partial differential equations using lifting scheme.

Wavelet theory is a recently developed promising tool in science and engineering research; particularly wavelets are successfully used in fast algorithms for easy implementation. In this paper, we present wavelet-based numerical solutions of elliptic boundary value problems encountered in mathematical physics, using lifting scheme. Here we used orthogonal and biorthogonal wavelets to demonstrate the effectiveness and efficiency of the proposed technique. The proposed scheme speeds up convergence in lesser computational time. Numerical examples are given to prove the robustness of proposed technique. [ABSTRACT FROM AUTHOR]