Answer to Question #139488 in Differential Equations for Nikhil Singh

Question

Outline briefly the fundamental idea of jacobi's method of solving non-linear partial differential equation f(x,y,z,p,q)=0. Give its advantage over charpit's method of solving the same equation.

Answer 1

In numerical linear algebra, the Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.

Advantages of the Jacobi method. It is simple and numerically robust. Each iteration is quite fast.