Second Order Numerical Integration w/ Neumann Boundary Conditions

a2009
Messages
22
Reaction score
0
I hope this is the right place to post this question.

I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C.

I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative I'm stuck.

If anyone could point me in the right direction, or refer me to a text that discusses this problem I'd really appreciate it.
 
Physics news on Phys.org
I can add more to this later. But for now check the Numerical Recipe website. www.nr.com Check in the section that has the older versions of the book in pdf format.
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
Back
Top