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Matlab is the tool for all numerical computation and now a days it is widely used as Matlab programming language and simulation and use to project it on hardware as advance Matlab like Image Processing, Control Engineering.
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Here is an example of solved Matlab Problem solved by our Matlab Expert
Solving a system of Linear Differential Equations using Matlab Programing.
function f = plot_xyz_t()
% this function plot t vs x, y,z
% Uses ODE45 to solve
% dx_dt(1) = s*(x(2)-1*x(1))
% dx_dt(2) = x(1)*(p-x(3))-x(2)
% dx_dt(3) = x(1)*x(2)-b*x(3)
% All equations in terms of coefficients
%dX/dt = [-s s 0; p , set an error
options=odeset('RelTol',1e-6);
%initial conditions
Xo = [-8;8;27]
%timespan
tspan = [0,40]
%call the solver
[t,X] = ode45(@TestFunction,tspan,Xo,options);
%plot the results
hold on
plot(t,X(:,1)),':';plot(t,X(:,2),'-ro');plot(t,X(:,3),'-bo')
% plot(X(:,1),X(:,2)),':';plot(X(:,2),X(:,3),'-ro');plot(X(:,1),X(:,3),'-bo')
legend('x','y','z');ylabel('x,y,z, p 99.96');xlabel('t')
hold on
plot(X(:,1),X(:,2)),':';plot(X(:,2),X(:,3),'-ro');plot(X(:,1),X(:,3),'-bo')
legend('x','y','z');ylabel('x,y,z, p =99.96');xlabel('t')
return
function [dx_dt]= TestFunction(t,x)
%dx_dt(1) = dx/dt
% dx_dt(2) = dy/dt
% dx_dt(3) = dz/dt
% x(1) = x
% x(2) = y
% x(3) = z
s = 10 % sigma
b = 8/3 % beta
p = 99.96 % row%a function which returns a rate of change vector
%M = [-1,-1;...
%1,-2]
%dx_dt = M*x;
dx_dt1 = 10*(x(2)-1*x(1))
dx_dt2 = x(1)*(p-x(2))-x(2)
dx_dt3 = x(1)*x(2)-b*x(3)
dx_dt = [dx_dt1;dx_dt2;dx_dt3]
return
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