ODE45 WITH MATRIX V AND TIME

Hi

I have a function

function xprime = tdofssfun(t,x)

global  a b u k x0  T  v1  
xprime = (a-b*k)*x -(a-b*k)*[ v1;0;0];

end

THEN

[t,x] = ode45('tdofssfun',tspan,x0,options);

and I want solve the equation where a 3*3 matrix, b 3*1 matrix k1*3 matrix

In general i can solve this equation if v1 is constant or has function with time

but the problem I have matrix of value for v1 and evrey value calculating at on time so i want to solve this equation

as example

v1=[0.2 0.5 0.6 0.9]

with time

t=[0.5 1 1.5 2]

Thx

Answer 1

[Walter Roberson]

Instead of using global, parameterize your function. Then it becomes easy to loop over an array of values.

[rami]

The problem is time: The functiom must dolve ODE45 for matrix V1, according to the time matrix, which mean the first value for v1 must solving according time from 0 to first value of time matrix, where second value of v2 must running with time betweem first value and second value for time matrix and so

[Walter Roberson]

function xprime = tdofssfun(t, x, a, b, u, k, x0, T, v)
  xprime = (a-b*k)*x - (a-b*k)*[ v;0;0];     
end

for N = 1 : length(v1) - 1
  [t{N}, x{N}] = ode45(@(t,x) tdofssfun(t, x, a, b, u, k, x0, T, v1(N)), tspan(N:N+1), x0, options);
end

You should also be considering optimization by pre-calculating common expressions.

[rami]

I try this, but when I plot it for v consist of 57 value with time from 1 to 57, and after plot it I have result that simulate all value for v ( in my example first value 0 and end 18) with time between 56 to 57. Which mean that calculate all value of v in on one period, and repeat it. While what i need that function solve v(1)for period between 0-1, then v(2) between period 1-2 and so on. then plot result for v according time from 1-57

for plot i use

plot(t{N}, x{N}(:,1))

[rami]

however this all program:

   function xprime = tdofssfun(t, x, a, b,  k, x0,  v)
    xprime = (a-b*k)*x - (a-b*k)*[ v;0;0]

   end

   a=[0 1 0;0 0 1; -1.9*10^5 -2*10^5 -2.4*10^5];

% define the input matrix, b 

      b=[0 ;0 ;6*10^5];

%  define the output matrix for transient response, c, displacements only 

   c = [1 0 0]; 
   k=[   110 16 0];

   v=[ 0    0.0245    0.0736    0.1471    0.2452    0.3678    0.5149    0.6865    0.8827    1.1034    1.3486    1.6183    1.9125    2.2313    2.5745    2.9423  3.3346    3.7515    4.1928    4.6587    5.1491    5.6640    6.2034    6.7674    7.3558    7.9688    8.6063    9.2684    9.9304   10.5679   11.1809   11.7693 12.3333   12.8727   13.3876   13.8780   14.3439   14.7852   15.2021   15.5944   15.9622   16.3072   16.6504   16.9692   17.2634   17.5331   17.7783   17.9990 18.1952   18.3668   18.5139   18.6365   18.7346   18.8081   18.8572   18.8817   18.8817];

    tspan = [     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27 28    29    30    31    32    33    34    35    36    37    38    39    40    41    42    43    44    45    46    47    48    49    50    51    52    53    54 55    56    57];  

    x0 = [0 0 0]';    %  initial condition vector, note transpose
    options = [];    %  no options specified for ode45 command 

   for N = 1 : length(v) - 1
    [t{N}, x{N}] = ode45(@(t,x) tdofssfun(t, x, a, b,  k, x0,  v(N)), tspan(N:N+1), x0, options);
  end

   figure(1)
    plot(t{N}, x{N}(:,1))

[Walter Roberson]

I would need to run the code to test (which I cannot do this week), but what I suspect you want as output is

tvals = vertcat(t{:});
xvals = vertcat(x{:});
x1vals = xvals(:,1);
plot(tvals, xvals);