Difference methods for solving nonlinear equations of mathematical physics

Difference Methods for Solving Nonlinear Equations of Mathematical Physics 

In this chapter the new difference schemes are constructed for the quasilin-ear heat conduction equation and equations of gas dynamics with placing a special emphasis on iterative methods available for solving nonlinear difference equations. Among other things, the convergence of Newton s method is established for implicit schemes of gas dynamics. 

The stationary problem. To avoid misunderstanding, we concentrate primarily on the simplest problem, the statement of which is related to the stationary heat conduction problem with nonlinear sources  

An excellent start in this direction is to introduce on the segment 0 a 1 an equidistant grid = x = ih, i = 0,1, N, hN = 1 and proceed to design the difference scheme 

Marcel Dekker, Inc. 270 Madison Avenue, New York, New York 10016 

It seems clear that scheme (2) generates an approximation of order 2  

What is more, a solution of the difference problem (2) is bounded, so that 

In this regard, Newton s method suits us perfectly in connection with solving the nonlinear difference equation (2). It is worth recalling here its algorithm  

---

Difference methods for solving nonlinear equations of mathematical physics... 

---