fred
Fredholm integral for dtau object.
Syntax
F = fred(varargin)
Description
F = fred(y, K) returns the matrix F that translates the Fredholm
integral term int_a^b(K(x, t)y(t)dt) into an orthogonal polynomial
basis.
Inputs
y = dependent tau variable (dtau object).
K = two variable function K(x, t) (char or numeirc matrix).
If K is char, then the coefficients will be automatically found.
If K is numeric column, then is related with coeff a of aP(x).
If K is numeric row, then is related with coeff a of aP(t).
If K is double matrix, then is related with coeff a of aP(x)P(t).
Output
F = matrix sized by [y.n y.n] in an orthogonal polynomial basis.
Example
y = dtau('TchebyshevU', [1 2], 5);
F = fred(y, 'cos(x+t)'); % F is the matrix that translates
% int_1^2(cos(x+t)y(t)dt) into
% the specified orthogonal basis.
See also
volt, diff and int.
F = fred(y, K) returns the matrix F that translates the Fredholm integral term int_a^b(K(x, t)y(t)dt) into an orthogonal polynomial basis.
Inputs
y = dependent tau variable (dtau object).
K = two variable function K(x, t) (char or numeirc matrix).
If K is char, then the coefficients will be automatically found.
If K is numeric column, then is related with coeff a of aP(x).
If K is numeric row, then is related with coeff a of aP(t).
If K is double matrix, then is related with coeff a of aP(x)P(t).
Output
F = matrix sized by [y.n y.n] in an orthogonal polynomial basis.
Example
y = dtau('TchebyshevU', [1 2], 5);
F = fred(y, 'cos(x+t)'); % F is the matrix that translates
% int_1^2(cos(x+t)y(t)dt) into
% the specified orthogonal basis.
See also
volt, diff and int.
F = matrix sized by [y.n y.n] in an orthogonal polynomial basis.
Example
y = dtau('TchebyshevU', [1 2], 5);
F = fred(y, 'cos(x+t)'); % F is the matrix that translates
% int_1^2(cos(x+t)y(t)dt) into
% the specified orthogonal basis.
See also
volt, diff and int.
volt, diff and int.