Trapezoidal method differential equation

[ShoxPhysics]

Hello,
I am working on a program to find the value of the current in a coil. This value satisfies the following equation:
y'=sin(2t)-[(e^y-1)/(e^y+1)]

which is of the form y'=f(t,y)

I know that in order to solve this I need to use the trapezoidal method to solve a differential equation, the formula is:
y_n+1=y_n+.5*h(f(t_n,y_n)+f(t_n+1,y_n+1) where h=t_n+1-t_n

I have found examples of the standard trapezoidal method but I do not think they will help because of the difference in the formulas. Can anybody give me some guidance here?

[Bourgond Aries]

ShoxPhysics wrote:

I know that in order to solve this I need to use the trapezoidal method to solve a differential equation, the formula is:
y_n+1=y_n+.5*h(f(t_n,y_n)+f(t_n+1,y_n+1) where h=t_n+1-t_n

I believe it's supposed to be: (check parenthesis)

y_n+1=y_n+.5*h(f(t_n,y_n)+f(t_n+1,y_n+1)) where h=t_n+1-t_n

[ats15]

A good explanation of what you want is at http://www.swarthmore.edu/NatSci/echeeve1/Ref/NumericInt/RK2.html

You start with an initial condition y₀ at t₀, and you want to find all y_n at t_n=t₀+n*h (you calculate y on a regular grid)

1. Create a temporary value for y₁, as y_1,temp=y₀+h*f(t₀,y₀)
2. Calculate the value at t₁ as y₁=y₀+0.5*h*(f(t₀,y₀)+f(t_1,temp,y_1,temp))

Now you have y₁. Repeat the same procedure to calculate y₂ and so on