From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci) Subject: Re: Method of lines Date: 3 Jan 2000 17:03:56 GMT Newsgroups: sci.math.num-analysis In article <3865FD0B.D6BAC49E@central.ntua.gr>, mc96118@central.ntua.gr writes: |> Hello , |> could someone please tell me what the method of lines is |> Many thanks in advance |> given a partial differential equation in a form like u_t = F(u,u_x,u_y,u_xx ,.....) or u_tt = F(....) such that F depends only on the function u and partial derivatives of u with respect to other variables than the variable t: replace the partial derivatives with respect to the other variables by finite differences on a grid and consider now the equation only on the grid points or make an "ansatz" u(t,...)=sum_i alpha_i(t)*phi_i(x,..) with finite element basis functions phi_i on a grid (in x-y-.. space), mulptiply by phi_j and integrate (over the domain of x,y,..) then you obtain in both cases a (large) system of ordinary differential equations in the variable t which you can integrate by the appropriate methods (taking stiffness, highly oscillatory solutions etc) into account. this is the basic idea of the methods of lines. hope that helps peter