Home > K25104 > ODEs > RK_stab_fun.m

RK_stab_fun

PURPOSE ^

derives the stability function for the Runge-Kutta method prescribed by b,c,A

SYNOPSIS ^

function [ R ] = RK_stab_fun( b,c,A )

DESCRIPTION ^

 derives the stability function for the Runge-Kutta method prescribed by b,c,A
 Input arguments:
   b, column vector holding the Runge-Kutta weights
   c, column vector holding the Runge-Kutta nodes
   A, matrix holding the coefficients a(i,j) which prescribe the method.
 Output arguments:
   R stability function

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [ R ] = RK_stab_fun( b,c,A )
0002 % derives the stability function for the Runge-Kutta method prescribed by b,c,A
0003 % Input arguments:
0004 %   b, column vector holding the Runge-Kutta weights
0005 %   c, column vector holding the Runge-Kutta nodes
0006 %   A, matrix holding the coefficients a(i,j) which prescribe the method.
0007 % Output arguments:
0008 %   R stability function
0009 
0010 % first check user inputs
0011 [Arows,Acols]=size(A);
0012 [brows,bcols]=size(b);
0013 [crows,ccols]=size(c);
0014 if Arows~=Acols;    
0015     error('matrix must be a square matrix');
0016 elseif bcols~=1 || ccols~=1;
0017     error('input must be column vectors');
0018 elseif brows~=Arows || crows~=Arows;
0019     error('dimensions do not match');
0020 end
0021 
0022 syms z      % create symbolic variable
0023 R=1+z*b'*inv(eye(Acols)-z*A)*ones(Acols,1); % construct stability function
0024 end
0025

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