Piecewise Lanczos' tau method for system of linear ODEs.

   a = tausyspw(x, y, ode_system, conditions, varargin)

   a = tausyspw(varargin) returns the coefficients, on basis P, of the 
   (n-1)th degree polinomial approximation yn = Pa, of the
   linear differential system dy/dx=f(t,y). The domain is automatically 
   decomposed in subintervals and the tau method is applied to each
   of these subintervals.

Inputs (required)
   x              = independent tau variable (itau object).
   y              = dependent tau variable (dtau oject).
   ode_system     = system of odes (cell of char).
   conditions     = problem conditions (cell of char).

Inputs (optional)
   pieces         = number of steps for piecewise approach (integer).
   exact_solution = exact solution (cell of char).
   step           = step on the x vector to show the results.
   precond        = preconditioner ('no', 'ilu', 'diag').
                    for 'ndiad' define: 'numbd' (number of diagonals);
                    for 'ilu' define: 'milu', 'typeilu', 'droptol', 
                                      'thresh' and 'udiag'
   solver         = linear system solver (check guide).
   apsol          = boolean varargin to show the graphical solution.
   resid          = boolean varargin to show the graphical error.
   coeff          = boolean varargin to show the coefficients a.
   spy            = boolean varargin to spy the T matrix.
   infor          = boolean varargin to show infomations at the CLI.
   saves          = name varargin to save the results at .mat.

   a              = approximate solution coefficients at basis P.

       [x, y] = tau('LegendreP', [0 2*pi], 10)
       a = tausyspw(x, y, ...
           {'diff(y1)-y2 = 0';'diff(y2)-y3 = 0';'diff(y3)+y2 = 0'}, ...
           {'y1(0)=0';'y2(0)=1';'y3(0)=0'}, 3);

See also
  tau, taupw, tausys and schursolver.