A modified wavelet multigrid method for the numerical solution of boundary value problems

Abstract

In this paper, we propose the modified wavelet multigrid method for the numerical solution of boundary value problems. Here we introduced the new intergrid operators (prolongation and restriction) based on Daubechies high pass and low pass filter coefficients for the sake of numerical efficiency. Numerical examples are presented to demonstrate the versatility of the proposed method in comparison with the standard methods viz multigrid and wavelet multigrid. Modified wavelet multigrid method is the robust technique for faster convergence with low computational cost which is justified through operator complexity, grid complexity, rate of convergence, condition number and error analysis.

Keywords:

• Multigrid method
• Wavelet multigrid
• Modified Wavelet multigird
• Differential equations