Tau Toolbox functions

Here are listed all functions found in Tau Toolbox. New changes from previous versions are informed as (New). You can save it as .m file separated or also download full .rar containg all functions.


@ctau
cos Cosine for ctau object.
cosh Hiperbolic cosine for ctau object.
ctau Class for coefficients of tau method.
exp Exponential for ctau object.
log Logarithm for ctau object.
minus Minus operation for ctau object.
mpower Power operation for ctau object.
mtimes Product operation for ctau object.
plot Plot for ctau object.
plus Plus operation for ctau object.
sin Sine for ctau object.
sinh Hiperbolic sine for ctau object.
uminus - Unitary minus operation for tau object.
uplus Unitary plus operation for ctau object.


@dtau
diff Differentiation for dtau object.
dtau Class for dependent tau variable.
fred Fredholm integral for dtau object.
int Integration for dtau object.
matrixC Builds the matrix C, related with the system [C; D]a = b.
matrixCsys Builds the matrix C, related with the system [C; D]a = b.
matrixN N matrix related with differentiation.
matrixO Sparse O matrix related with integration.
minus Minus operation for tau objects.
mrdivide Division operation for tau objects.
mtimes Product operation for tau objects.
plus Plus operation for tau objects.
uminus - Unitary minus operation for tau objects.
uplus Unitary plus operation for tau objects.
volt Volterra integral term.


@etau
diff Differenciation for empty tau object in systems.
etau Class to make zeros y in [a b] in terms of a polynomial basis.
fred Fredholm operator for empty tau object in systems.
int Integration for empty tau object in systems.
matrixN Differentiation for empty tau object in systems.
matrixO Integration for empty tau object in systems.
minus Minus operations for empty tau object in systems.
mrdivide Division for empty tau object in systems.
mtimes Multiplication for empty tau object in systems.
plus Sum for empty tau object in systems.
uminus Unitary minus for empty tau object in systems.
uplus Unitary sum for empty tau object in systems.
volt Volterra operator for empty tau object in systems.


@itau
cos Cosine for itau object.
cosh Hiperbolic cosine for itau object.
coshi Hiperbolic cosine by orthogonal interpolation for itau object.
coshm Hiperbolic cosine for matrix for itau object.
cosht Hiperbolic cosine by tau approximation for itau object.
cosi Cosine by orthogonal interpolation for itau object.
cosm Cosine for matrix for itau object.
cost Cosine by tau approximation for itau object.
exp Exponential for itau object.
expi Exponential by orthogonal interpolation for itau object.
expm Exponential for matrix for itau object.
expt Exponential by tau approximation for itau object.
itau Class for independent tau variable.
linspace Linear space for itau object.
log Logarithm for itau object.
logi Logarithm by orthogonal interpolation for itau object.
logm Logarithm for matrix for itau object.
logt Logarithm by tau approximation for itau object.
matrixM Sparse M matrix.
minus - Minus operation for tau object.
mpower Power operation for tau object.
mtimes Product operation for tau object.
plus Plus operation for tau object.
pol Polynomial evaluation.
pow2orth Change from power series to orthogonal basis.
powMrec Power of M matrix by recurrence.
sin Sine for itau object.
sinh Hiperbolic sine for itau object.
sinhi Hiperbolic sine by orthogonal interpolation for itau object.
sinhm Hiperbolic sine for matrix for itau object.
sinht Hiperbolic sine by tau approximation for itau object.
sini Sine by orthogonal interpolation for itau object.
sinm Sine for matrix for itau object.
sint Sine by tau approximation for itau object.
sqrt Square root for itau object.
sqrti Square root by orthogonal interpolation for itau object.
sqrtm Square root for matrix for itau object.
sqrtt Square root by tau approximation for itau object.
uminus - Unitary minus operation for tau object.
uplus Unitary plus operation for tau object.


@rtau
cos Cosine by tau approximation for rtau object.
cosh Hiperbolic cosine by tau approximation for rtau object.
exp Exponential by tau approximation for rtau object.
log Logarithm by tau approximation for rtau object.
minus Minus operation for rtau object.
mpower Power operation for rtau object.
mtimes Product operation for rtau object.
plus Plus operation for ctau object.
rtau Class to rigth member of tau problem.
sin Sine by tau approximation for rtau object.
sinh Hiperbolic sine by tau approximation for rtau object.
uminus - Unitary minus operation for rtau object.
uplus Unitary plus operation for rtau object.


BuildOrthogonalBasis
chebyshevTpoints Chebyshev points in [a b].
chebyshevUpoints Chebyshev points in [a b].
gegenbauerCpoints GegenbauerC points in [a b].
legendrePpoints Legendre points in [a b].
orth2powmatrix Orthogonal to power matrix.
orthobasispoints Orthogonal basis points in [a b].
plotpoly Plot orthogonal polynomials.
polbesselY Bessel polynomial basis in unitary circle.
polchebyshevT Chebyshev polynomial basis (T) in [-1 1].
polchebyshevTab Chebyshev polynomial (T) basis in [a b].
polchebyshevU Chebyshev polynoamil basis (U) in [-1 1].
polchebyshevUab Chebyshev polynomial (U) basisin [a b].
polgegenbauerC Gegenbauer polynomial basis in [-1 1].
polgegenbauerCab Gegenbauer polynomial basis in [a b].
polhermiteH Hermite polynomial basis in [-Inf Inf].
pollaguerreL Laguerre polynomial basis in [0 Inf].
pollegendreP Legendre polynomial basis in [-1 1].
pollegendrePab Legendre polynomial basis in [a b].
pow2orthmatrix Power to orthogonal matrix.
shift2ab Change interval of orthogonality to [a b].


Examples
dna2 This .m is an m-script.
linear_ide_fredholm_Hosseini2002 This .m is an m-script.
linear_ide_fredholm_non_polynomial_coefficients This .m is an m-script.
linear_ide_fredholmvolterra This .m is an m-script.
linear_ide_fredholmvolterra_2 This .m is an m-script.
linear_ide_fredholmvolterra_basic This .m is an m-script.
linear_ide_fredhom This .m is an m-script.
linear_ide_volterra This .m is an m-script.
linear_ide_volterra_Hosseini2002 This .m is an m-script.
linear_ide_wikipedia This .m is an m-script.
linear_ie_volterra_Yang2013Rabbani2007_ex1 This .m is an m-script.
linear_ie_volterra_Yang2013Rabbani2007_ex2 This .m is an m-script.
linear_ode This .m is an m-script.
linear_ode_Legendre This .m is an m-script.
linear_ode_OlverTownsend This .m is an m-script.
linear_ode_bvp_piecewise This .m is an m-script.
linear_ode_sign_function_with_non_plynomial_coefficients This .m is an m-script.
linear_ode_sign_function_with_polynomial_coefficients This .m is an m-script.
linear_ode_stiff_OlverTownsend_paper This .m is an m-script.
nonlinear_ide_fredholm_Dehghan2012_ex1 This .m is an m-script.
nonlinear_ide_fredholm_Dehghan2012_ex2 This .m is an m-script.
nonlinear_ide_system_volterra_Abbasbandy2009_1 This .m is an m-script.
nonlinear_ide_system_volterra_Abbasbandy2009_2 This .m is an m-script.
nonlinear_ode_basic This .m is an m-script.
nonlinear_ode_chenlee This .m is an m-script.
nonlinear_ode_halvorsen This .m is an m-script.
nonlinear_ode_lambertWfunction This .m is an m-script.
nonlinear_ode_lambertWfunction_basic This .m is an m-script.
nonlinear_ode_loktavolterra This .m is an m-script.
nonlinear_ode_lorenz This .m is an m-script.
nonlinear_ode_lorenz_basic This .m is an m-script.
nonlinear_ode_rossler This .m is an m-script.
nonlinear_ode_thomas This .m is an m-script.
nonlinear_ode_three_scroll_unified This .m is an m-script.
nonlinear_ode_three_scroll_unified_basic This .m is an m-script.
nonlinear_ode_with_and_whithout_coef_linearisation This .m is an m-script.
nonlinear_ode_with_cos_as_nonlinearity This .m is an m-script.
nonlinear_ode_with_cos_as_nonlinearity_basic This .m is an m-script.


FunOfCoef4nonlinear
cosho Orthogonal hiperbolic cosine.
coso Orthogonal cosine.
expo Orthogonal exponential.
logo Orthogonal logarithm.
sinho Orthogonal hiperbolic sine.
sino Orthogonal sine.
sqrto Orthogonal square root.


FunctionOfMatrix
coshm Matrix hiperbolic cosine.
cosht Cos by tau approximation.
cosm Matrix cosine.
cost Cos by tau approximation.
expt Exp by tau approximation.
logt Log by tau approximation.
sinhm Matrix hyperbolic sine.
sinht Sinh by tau approximation.
sinm Matrix sine.
sint Sin by tau approximation.


OperatorsEvaluation
taudiff Tau derivative evaluation.
taufred Tau Fredholm evaluation.
tauint Tau integration evaluation.
tauvolt Tau Volterra evaluation.
verapproximation Verify approximation.


OrthogonalEvaluation
orthoval Orthogonal evaluation.
orthovalM Orthogonal evaluation for matrices.
orthovalMj j-th orthogonal evaluation for M matrices.
orthovald Orthogonal (and its derivatives) evaluation.
orthovalv Orthogonal evaluation.
orthovalvj j-th orthogonal evaluation.


OrthogonalInterpolation
interporth Orthogonal polynomial interpolation.
interporth2 Orthogonal polynomial interpolation for 2 dimension.
interporth2_error Error in the orthogonal interpolation of F(x,t).
interporth2inc Incremental orthogonal polynomial interpolation for 2D.
interporthinc Incremental orthogonal polynomial interpolation.


ProductOfPolynomials
chebypolypow Power of Chebyshev polynomials.
chebypolyprod Product of Chebyshev polynomials.
legpolypow Power of Legendre polynoamials.
legpolyprod Product of Legendre polynomials.
orthopolyprod Product of orthogonal polynomials.


TauGui
createmfile_advanced_ode Creates an m-file for ode in advanced mode.
createmfile_advanced_ode_pw Creates an m-file for ode (piecewise)
createmfile_advanced_sys Creates an m-file for systems of odes
createmfile_advanced_sys_pw Creates an m-file for systems of odes
createmfile_beginner Creates an m-file for the problem in beginner mode.
findsolver Find the appropriate solver from taugui.
getalldata Get all data.
informations Informations for taugui.
taugui TAUGUI MATLAB code for taugui.fig


TauSolvers
schur_iter Schur iterative.
schur_luinc LU incemental.
schur_luinc2 LU incemental.
schur_nflu Schur with non fixed LU.
schurc Schur complements.
schursolver Iterative Lanczos' tau method based on Schur complements.
schursolverpw Iterative Lanczos' tau method based on Schur complements.
tauode Lanczos' tau method for linear ODEs.
tauodenewton Tau method for linearized problems by newton iterations.
tauodepw Piecewise Lanczos' tau method for linear ODEs.
tauodepwpvf Piecewise Lanczos' tau method for linear systems of BVP.
tausolver Lanczos' tau method for linear differential problems.
tausys Lanczos' tau method for system of linear ODEs.
tausysnewton Tau method for linearized problems by newton iterations.
tausyspw Piecewise Lanczos' tau method for system of linear ODEs.


Tests
TEST_Mrec_vs_Mformal This .m is an m-script.
TEST_Mrec_vs_Mformal_problem This .m is an m-script.
TEST_coef_fun_by_Schurcomplements This .m is an m-script.
TEST_coeflinearization_vs_convolution This .m is an m-script.
TEST_differents_kind_of_orthoval This .m is an m-script.
TEST_invVAV_vs_recA This .m is an m-script.
TEST_invVAV_vs_recA_problem This .m is an m-script.
TEST_invVAV_vs_recA_problem2 This .m is an m-script.
TEST_invVAV_vs_recA_spy This .m is an m-script.
TEST_invV_vc_W This .m is an m-script.
TEST_invV_vc_W_problem This .m is an m-script.
TEST_polyval_vs_orthoval This .m is an m-script.
TEST_polyval_vs_orthoval_kernel This .m is an m-script.


Tools4Tau
Cauchy_error norm-2 of the error between two approximations with
MbyLU M preconditioner by LU factorization.
altura Find the D height.
basis2basis change of basis.
changesupc Change the conditions format.
colorR2B Color scale from red to blue.
deriveP Derivative of matrix V.
domain2 Creates a two dimentional domain.
eorth ith vector from orthogonal basis.
epow ith vector from canonical basis.
evalonly Evaluate selected variables in a string.
evalonlynewton Evaluate selected variables in a string.
fc Functional coefficient.
findint Find integral terms.
findkernel Find kernel of integral term.
fun2orth Funtion to orthogonal polynomial basis.
isivp Checks for initial value problems
matrixT T matrix related with Ta=b.
maxerror Maximal error between a function and its approximation.
mno M N and O matrices.
myspy Plots a 3D spy of matrix T
poly2str Converts multivariate polynomials from arrays to strings.
prodcoef Product of coefficients.
readcondcell Read conditions.
readcondcellsys Read conditions for systems.
reorg2poly Reorganize to polynomial.
reorg2vec Reorganize to vector.
solvingthesystem Solve a system of linear algebraic equations.
spliteq Split equation.
str2poly Converts multivariate polynomials from strings to arrays.
tau Creates (independent and dependent) tau variables.
tauc Tau clearing.
tausettings Tau settings.
tausystem Matrix T and vector b.