Решение ДУ методом конечных разностей

[StefanSt.]

Hello to all of you
I hope, that in English it will easier for me to write my question.
And here it is - I have solve an ordinary differential equation, by use of "finite difference method". This equation describes the velocity of a freely fallin spherical drop as a fonction of a "contact time".
The symbol for velocity is "U".
Contact time is "t".
Here is the equation:
$\frac{dU}{dt} = 9.7819 - 0.3762U^2$

I'use the forward difference approximation: $\frac{U_{i+1} - U_i} {h} = 9.7819 - 0.3762U^2_i$
and when I develop it, I obtain: $U_{i+1} = 9.7819h - 0.3762hU^2_i + U_i$
then $U_{i+1} = 9.7819h + U_i(1 - 0.3762hU_i)$
My question is relied to the second degree of U and it's development in finite difference approximation. This equation is going to be resolved by a Fortran program. I've alreday done an algorythm for equations describing radial diffusion in a sphere, so I think, that this one will not be that hard. But I don't get, how to describe this ordinary diff. equation.
Once I do it, I have to implement the "value" of U, into an integral, which gives me a distance. But first of all the equation :)
I know, that this is easy for you, but for me is difficult.
Thank you all!!!

[Toucan]

Тема перемещена в Карантин.

Запишите формулы в соответствии с требованиями Правил форума, т.е. в $\TeX$.
Краткие инструкции можно найти здесь: topic8355.html и topic183.html.
Кроме этого, в теме Видео-пособия для начинающих форумчан можно посмотреть видео-ролик "Как записывать формулы".

Некоторые места Вашего сообщение понять довольно сложно; если у Вас проблемы с русским языком, Вы можете сформулировать задачу по-английски.

После того как исправите сообщение, сообщите об этом в теме Сообщение в карантине исправлено.

[Toucan]

Вернул.

[Dan B-Yallay]

StefanSt. в сообщении #563365 писал(а):

My question is relied to the second degree of U and it's development in finite difference approximation.

So, what is the question exactly?