solving a differential equation with NEWTON....

myway

Hi,

I want to solve a differential equation y'=B*y-A*C*exp(B*x)*sin(C*x) using Euler (implicit) and a Newton-like method.

But let me give you a short introduction into my problem.

Euler (implicit) is defined as: u_i+1 = u_i + du/dx_i+1 * Dx

Since not all terms on the right hand side are known, a (system of equations) must be solved, which is:

F(u_i+1) = u_i - (u_i+1 + Dx * (B*u_i+1 - A*C*exp(B*(x+Dx))*sin(C*(x+Dx))))

Some people told me, I could solve the problem with the Newton-procedure. The principle is clear to me. But can anybody tell me how I have to calculate u*, which is the value of u where the tangent intercepts the x-axis??? I need that value to calculate the next tangent.

Thanks for your patience.