|May 15, 2006, 02:05||
solving a differential equation with NEWTON....
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.
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