Group Abstract Group Abstract

Message Boards Message Boards

Solve system of differential equations numerically?

Alex B
Posted 5 years ago

Hello all,

I am currently trying to numerically analyze the system of differential equations below. I am struggling to solve g'(t), as it involves the partial differential equation w'(g(t)). My goal is to generate a simple plot that shows how the system changes over time. Attached is my code. Any suggestions would be greatly appreciated!

h'(t) = y(t)*(1-h(t))*g(t) - a*h(t)

y'(t) = y(t)*b*(1-c)*w(h(t)) - y(t)*d*(x(t)+y(t)),        where w(h(t)) = h(t) - (1 - h(t))*g(t)

g'(t) = V*w'(g(t))

Alex

Attachments:
Test.nb
POSTED BY: Alex B
3 Replies
Sort By:
POSTED BY: Hans Dolhaine

Let's start with $$ W(g(t)) = g^2(t).$$ Differentiate both side of the above equation using the chain rule on the left-hand side: $$ g'(t) W'(g(t)) = 2 g'(t) g(t).$$ If we assume that the derive of $g$ does not vanish, the last equation implies that $W'(g(t)) = 2g(t)$. Now the last equation in your system becomes $$g'(t) = 2Vg(t).$$ By separating the variables, the last equation yields $$ g(t) = Ae^{2Vt},$$ where $A$ is an arbitrary constant.
POSTED BY: Ta'a Nwa Dombou

Substituting for w[h[t]] is straightforward, but it is not clear to me how the solver will be able to numerically compute w'[g[t]].
POSTED BY: Daniel Lichtblau
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard