Using ode to solve a specific differential equation
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I need help solving this specific differential equation using ode45 in MATLAB. The differential equation is k*(dT/dt)= A*Q*(1-b(T)) - S*c*E*(T^4). We have all of the values but I need code to solve and plot different solutions to the ode.
2 个评论
William Rose
2021-11-8
@Allison Reynolds, what have you done so far? When you say you need to solve and plot different solutions, what do you mean? Different initial conditions? Different values for the constants?
Please post what you have done so far, including values for the initial conditions and the constants.
William Rose
2021-11-8
@Allison Reynolds, does Q(1-b(T)) mean Q*(1-b*T))? If not, then specify what the functions b and Q are.
回答（1 个）
Try these —
% k*(dT/dt)= A*Q(1-b(T)) - S*c*E*(T^4)
odefcn = @(t,T,a,b,c,E,k,Q,S) (a*Q*(1-b*T) - S*c*E*(T^4))/k; % If 'Q' Is A Scalar
a = rand;
b = rand;
c = rand;
E = rand;
k = rand;
Q = rand;
S = rand;
tspan = [0 20];
ic = 0.42;
[t,T] = ode45(@(t,T)odefcn(t,T,a,b,c,E,k,Q,S), tspan, ic);
figure
plot(t,T)
grid
odefcn = @(t,T,a,b,c,E,k,Q,S) (a*Q(1-b*T) - S*c*E*(T^4))/k; % If 'Q' Is A Function
a = rand;
b = rand;
c = rand;
E = rand;
k = rand;
S = rand;
Q = @(x) sin(x) .* cos(x); % Make Something Up
tspan = [0 20];
ic = 0.42;
[t,T] = ode45(@(t,T)odefcn(t,T,a,b,c,E,k,Q,S), tspan, ic);
figure
plot(t,T)
grid
Experiment to get the desired result.
.
2 个评论
William Rose
2021-11-8
Nice compact and elegant solution by @Star Strider
Star Strider
2021-11-8
Thank you!
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