Solving a system of differential equations using central difference approximations

Good day,

I am having a bit a trouble solving this system:

Incorporating the following central difference approximations:

I've made an attempt to solve this using a method I use when I encounter linear de's rather than a system. I don't know if its valid in a system case...

First thing, I shifted the indices for

ie.

Substituting these into the :

Where,

From here I let , sub it into the equation and basically solve for n.

I get a solution for that contains like 6 constants.

I use this to solve for which results in a long solution with many square roots.

As I mentioned I'm highly doubtful if this is actually how you do it... Any help would be greatly appreciated.

Thanks

Re: Solving a system of differential equations using central difference approximation

Quote:

Originally Posted by

**MrPhil** Good day,

I am having a bit a trouble solving this system:

Incorporating the following central difference approximations:

I've made an attempt to solve this using a method I use when I encounter linear de's rather than a system. I don't know if its valid in a system case...

First thing, I shifted the indices for

ie.

Substituting these into the

:

Where,

From here I let

, sub it into the equation and basically solve for n.

I get a solution for

that contains like 6 constants.

I use this to solve for

which results in a long solution with many square roots.

As I mentioned I'm highly doubtful if this is actually how you do it... Any help would be greatly appreciated.

Thanks

Seems like a lot of work, who said to use central differences?

CB

Re: Solving a system of differential equations using central difference approximation

Quote:

Originally Posted by

**CaptainBlack** Seems like a lot of work, who said to use central differences?

CB

In a lecture, we had two examples(that weren't systems) and solved them using finite difference methods. We were left to attempt this question along with the two central difference approximations. I would have used Adam's Method to solve something like this.

Re: Solving a system of differential equations using central difference approximation