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> Using Matlab m-files




EXPMATX.OMS

Script File:
# Description
# Uses matrix exponential to compute sine and cosine functions.
#
clear
# coefficient matrix for dy / dt = A * y
A = { [ 0., 10. ] , [ - 10., 0. ] }     
# matrix exponential of A
E = expmat(A, 1e-4, 6)                  
# value of y(1) = sin(10 * t) and
# y(2) = cos(10 * t) at t = 0.
y = {0., 1.}                            
# format for output
format real "f10.5"
# header for output
header = "t, sin(10 * t), cos(10 * t), y(1), y(2)"
header = align(header, ", ", [10, 11, 11, 11, 11])
write("screen", header)
for i = 1 to 10 begin
	# value of time
	t = real(i)
	# value of y using matrix exponential
	y = E * y
	#
	write("screen", [t, sin(10 * t), cos(10 * t), y'])
end
	  

Output:
t         sin(10     *          t)         cos(10     
   1.00000   -0.54402   -0.83907   -0.54402   -0.83907
   2.00000    0.91295    0.40808    0.91295    0.40808
   3.00000   -0.98803    0.15425   -0.98803    0.15425
   4.00000    0.74511   -0.66694    0.74511   -0.66694
   5.00000   -0.26237    0.96497   -0.26237    0.96497
   6.00000   -0.30481   -0.95241   -0.30481   -0.95241
   7.00000    0.77389    0.63332    0.77389    0.63332
   8.00000   -0.99389   -0.11039   -0.99389   -0.11038
   9.00000    0.89400   -0.44807    0.89400   -0.44808
  10.00000   -0.50637    0.86232   -0.50636    0.86232
	  


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