## tauode

Lanczos' tau method for linear ODEs.

Lanczos' tau method for linear ODEs.

a = tauode(x, y, ode, conditions, varargin)

a = tauode(varargin) returns the coefficients, on basis P, of the (n-1)th degree polinomial approximation yn = Pa, of the linear differential equation dy/dx=f(t,y).

x = independent tau variable (itau object). y = dependent tau variable (dtau oject). ode = ordinary differential equation (char). conditions = problem conditions (cell of char).

exact_solution = exact solution (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. apsol = boolean varargin to show graphically the solution. resid = boolean varargin to show graphically the error. coeff = boolean varargin to show the coefficients a. spy = boolean varargin to spy the T matrix. saves = name varargin to save the results at .mat.

a = approximate solution coefficients at basis P.

tauodepw, tausys, tausyspw and schursolver.