Opuscula Math. 28, no. 2 (2008), 163-178
On the Chaplyghin method for first order partial differential equations
Abstract. Classical solutions of initial problems for nonlinear first order partial differential equations are considered. It is shown that under natural assumptions on given functions, there exist Chaplyghin sequences and they are convergent. Error estimates for approximate solutions are given. The method of characteristics is used for the construction of approximate solutions.
Keywords: characteristics, Newton method, Chaplyghin sequences, initial problems.
Mathematics Subject Classification: 35A35, 35F25, 65J15.
- Received: 2007-10-15.
- Revised: 2007-11-08.
- Accepted: 2007-11-14.