parallel computing apply to my problem

clc;
clear all;
close all;
tic;
N=10;
a=zeros(1,N+1);
b=zeros(1,N+1);
syms t a b

a(1)=2;b(1)=-3;
for i=1:7
    v1=(a(i)*t+5*a(i)*t^2+30*b(i)*t);
    v2=(b(i)*t-20*b(i)*t^3+30*a(i)*b(i)*t);
    a(i+1)=diff(v1,t);
    b(i+1)=diff(v2,t);
end
toc
fplot(v1,[0 0.1],'b');

;;;i want to go for loop till 250 for above kind of problem when there are 8 equations means v1,v2...v8.it is taking so much of time and sometimes matlab is not responding.Please help me how can i wrote that proble with parallel computing or any some other simple programmimg

Answer 1

[Walter Roberson]

Change

    a(i+1)=diff(v1,t);
    b(i+1)=diff(v2,t);

to

    a(i+1) = expand(diff(v1,t));
    b(i+1) = expand(diff(v2,t));

Although the expand() operation takes some time, it reduces the complexity of the expressions significantly, leading to much much faster diff() in the following steps.

Answer 2

[Matt J]

Skipping the symbolic operations will speed things up,

tic;

    t=linspace(0,0.1,1000)';
    tsquared=t.^2;
    
    [a,b]=deal(nan(numel(t), 251 ));
    a(:,1)=2;b(:,1)=-3;
    
    for i=1:250
    
        ai=a(:,i); bi=b(:,i);
        
        a(:,i+1) = ai.*(1 + 10*t) + 30*bi;
        
        b(:,i+1) = bi.*(1 - 60*tsquared) + 30*ai.*bi;
        
    end

   v1=a(:,7);

toc

Elapsed time is 0.059089 seconds.

plot(t,v1,'b');

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