Numerical PDE
Write a MatLab program to solve this equation numerically. Don't use MATLAB'S built-in functions, please.
dy/dt = e ^ y − αy, y(0) = 0 where α > 0 is a parameter.
Discuss the equilibrium points, the values when e^y = αy and the case when α = 0
`Hey,
Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.
clc
clear all
close all
alpha=1;
f=@(t,y) exp(y)-alpha*y;
[T,Y]=eulerSystem(f,[0,1.2],0,0.01);
plot(T,Y)
function [t,y]=eulerSystem(Func,Tspan,Y0,h)
t0=Tspan(1);
tf=Tspan(2);
N=(tf-t0)/h;
y=zeros(length(Y0),N+1);
y(:,1)=Y0;
t=t0:h:tf;
for i=1:N
y(:,i+1)=y(:,i)+h*Func(t(i),y(:,i));
end
end
Kindly revert for any queries
Thanks.
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