Home > K25104 > ODEs > boundary_locus.m

boundary_locus

PURPOSE ^

Uses the boundary locus method to identify the boundary

SYNOPSIS ^

function [ z ] = boundary_locus( rho,sigma,n )

DESCRIPTION ^

 Uses the boundary locus method to identify the boundary 
 of the linear stability region of the general multistep method 
 described by the polynomials rho and sigma.
 Input arguments:
   rho, sigma, column vectors whose elements are the coefficients
     of the defining polynomials in descending powers.
   n, number of plot points
 Output arguments:
   z, points on paramterised curve

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [ z ] = boundary_locus( rho,sigma,n )
0002 % Uses the boundary locus method to identify the boundary
0003 % of the linear stability region of the general multistep method
0004 % described by the polynomials rho and sigma.
0005 % Input arguments:
0006 %   rho, sigma, column vectors whose elements are the coefficients
0007 %     of the defining polynomials in descending powers.
0008 %   n, number of plot points
0009 % Output arguments:
0010 %   z, points on paramterised curve
0011 
0012 % check user inputs
0013 [a,b]=size(rho);
0014 [c,d]=size(sigma);
0015 if b~=1 || d~=1;
0016     error('inputs must be column vectors');
0017 elseif a~=c;
0018     error('inputs must be the same length');
0019 end
0020 
0021 x=linspace(0,2*pi,n);    % initialize range of the parameter
0022 
0023 num = polyval(rho,exp(1i*x));
0024 denom = polyval(sigma, exp(1i*x));
0025 z = num./denom;
0026 end
0027 
0028 
0029

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