Efisiensi Penggunaan V-cycle Dalam Metode Fungsi Walsh Untuk Menyelesaikan Persamaan Integral Fredholm Linear

摘要

Uljanov and Blyth have developed a new numerical method for the solution of linear Fredholm integral equations using Walsh functions. The approximate solution is constructed by rewriting the functions as truncated (to m terms) Walsh series and the kernel as truncated double Walsh series. For the equations, this method gives linear systems. The systems then solved using Gauss elimination. In order to improve the efficiency, the idea of multigrid, especially v-cycle, is proposed to solve the linear systems. Here, numerical experiment with standard test problems for numerical solution of linear Fredholm integral equations show that this approach is effective in improving the efficiency of the Walsh function method.