حل مشكلة في الماثلاب حل معادلتين تفاضلية غير خطية لمتغربين في نفس الوقت x1 of t و x2 of t

اذا ممكن ارسل المعادلات بارفاق صور

طبعا هنا parameters وهي تكون معطى

I already wrote all parameters

T, t0, m, p1, p2, q1, q2, c1, c2, h=T/m and calculations of alpha , beta , v1, v2, x1_hat, x2_hat, u1_hat, u2_hat, l1, l2, L1, L2, a1, a2, a3, a4, a5

Just you need to solve two nonlinear differential equations of x1 and x2 in the same time

Solve dx1/dt and d x2/dt

And find u1 of t and u2 of t

This the code for the project

%% Numerical Example

% Clear data and figures

clc; clear all

% Initialize Parameter

T = 40; t0 = 0; m = 80; p1 = 1; q1 = 10; c1 = 25; p2 = 1; q2 = 10; c2 = 25;

h = T/m;

% Symbloic represetation

syms t

% Calculate alpha and beta

alpha = m*(m-1)/2; beta = m*(m-1)*(2*m-1)/6;

% Define Repair rate v1

v1 = @(t) 1/(1+t);

% Define Repair rate v2

v2 = @(t) 1/(1+t);

% Define Target Probability x1_hat

x1_hat = @(t) 1/(40+cos(t));

% x1_hat'

dx1_hat = matlabFunction(diff(x1_hat(t)));

% Define Target Probability x2_hat

x2_hat = @(t) 1/(40+cos(t));

% x2_hat'

dx2_hat = matlabFunction(diff(x2_hat(t)));

% Calculate u1_hat

u1_hat = @(t) (1/x2_hat(t))*(v1(t)*x1_hat(t) - dx2_hat(t));

% Calculate u2_hat

u2_hat = @(t) (1/(1 - x1_hat(t) - x2_hat(t)))*(v2(t)*x1_hat(t) + dx1_hat(t) + dx2_hat(t));

% Calculate L1(t),L2(t),l1(t)and l2(t)

L1(t) = @(t) p1*h^2*(alpha -beta*h*(v1(t)+v2(t)+u2_hat(t)))+2*h*m*((h*p1/4)+(c1/2))*(1- h*m*(v1(t0)+v2(t0)+u2_hat(t)));

L2(t) = @(t) beta*p1*h^3*(u1_hat(t)-u2_hat(t))+2*h^2*m^2*((h*p1/4)+(c1/2))*(u1_hat(t)-u2_hat(t));

l1(t) = @(t) p1*h^2*(alpha -beta*h*(v1(t)+v2(t)+u2_hat(t)))-beta*p2*h^3*v1(t)+2*h*m*((h*p1/4)+(c1/2))*(1- h*m*(v1(t0)+v2(t0)+u2_hat(t)))-2*h^2*m^2*((h*p2/4)+(c2/2))*v1(t);

l2(t) = @(t) beta*p1*h^3*(u1_hat(t)-u2_hat(t))+(alpha -beta*h*u1_hat(t))+(2*h^2*m^2*((h*p1/4)+(c1/2))*(u1_hat(t)-u2_hat(t)))-2*h*m*((h*p1/4)+(c1/2))*(1-h*m*u1_hat(t));

% Calculate a1(t), a2(t), a3(t), a4(t) and a5(t)

a1(t) = @(t) h*q1/4+(((p1/2)+(p2/2))*beta*h^3+((h*p1/4)+(c1/2))*h^2*m^2+((h*p2/4)+(c2/2))*h^2*m^2)*x2(t)^2;

a2(t) = @(t) h*q2/4+((beta*p1*h^3/2)+((h*p1/4)+(c1/2))*2*h^2*m^2)*(1-x1(t)-x2(t))^2;

a3(t) = @(t) (beta*p1*h^3+((h*p1/4)+(c1/2))*2*h^2*m^2)*(1-x1(t)-x2(t))*x2(t);

a4(t) = @(t) l1(t)*x2(t)*(x1(t)-x1_hat(t)) + l2(t)*x2(t)*(x2(t)-x2_hat(t));

a5(t) = @(t) L1(t)*(1-x1(t)-x2(t))*(x1(t)-x1_hat(t)) + L2(t)*(1-x1(t)-x2(t))*(x2(t)-x2_hat(t));

% Nonlinear Differential Equations

Nonlin_eq1 = @(t,x1) -(v1(t)+v2(t))*x1(t) + (u1_hat(t) + ((2*a2(t)*a4(t)-a3(t)*a5(t))/(a3(t)^2-4*a1(t)*a2(t))))*x2(t) + (u2_hat(t) + ((2*a1(t)*a5(t)-a3(t)*a4(t))/(a3(t)^2-4*a1(t)*a2(t))))*(1-x1(t)-x2(t));

Nonlin_eq2 = @(t,x2) -(u1_hat(t) + ((2*a2(t)*a4(t)-a3(t)*a5(t))/(a3(t)^2-4*a1(t)*a2(t))))*x2(t) + v1(t)*x1(t);