## tausyspw

Piecewise Lanczos' tau method for system of linear ODEs.

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.

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).

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);

tau, taupw, tausys and schursolver.