# Implementation implicit Gauss method
**URL:** https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912
**Category:** General Usage
**Tags:** question, nlsolve
**Created:** [September 1, 2024, 9:30pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912 "2024-09-01T21:30:41Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@khaledharizb](https://discourse.julialang.org/u/khaledharizb)
#### Post date: [September 1, 2024, 9:30pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/1 "2024-09-01T21:30:41Z")
I would like to implement Runge Kutta Gauss method. This method is implicit and need a nonlinear solver to do so. For that I define a fixed point solver `FixIter`, then the function `Gauss(f::Function,u₀,h,N)`
```julia
using LinearAlgebra
function FixIter(fun,u,tol)
while true
uold = u
u = fun(u)
norm(uold - u) > tol || break
end
return u
end
function Gauss(f::Function,u₀,h,N)
A = [0.25 0.25-√3/6 ; 0.25+√3/6 0.25]
b = [0.5, 0.5] ;
u = zeros(length(u₀),N+1)
u[:,1] = u₀;
for i in 1:size(u,2)-1;
g(K) = [f(u[:,i]+ h * (A[1,1] * K[1] + A[1,2] * K[2])),f(u[:,i]+ h * (A[2,1] * K[1] + A[2,2] * K[2]))]
K = FixIter(g,f(u[:,i]),1e-12);
u[:,i+1] = u[:,i] + h * b[1] * K[1] + h * b[2] * K[2];
end
return u;
end
```
My example is a pendulum problem with the vector field X = (y, \sin(x))
```julia
f(u) = [u[2], -sin(u[1])];
h=0.05; N=100;
x0=[1.,0.]
u = Gauss(f,x0,h,N)
```
However I get the following error
I appreciate any help you can provide.
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [September 1, 2024, 10:30pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/2 "2024-09-01T22:30:58Z")
if I’m understanding correctly, I believe this is just RadauIIA3 from OrdinaryDiffEq.jl
---
### Author:  [@khaledharizb](https://discourse.julialang.org/u/khaledharizb)
#### Post date: [September 1, 2024, 10:32pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/3 "2024-09-01T22:32:41Z")
No, this is 2-stages Gauss method [https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre\_method](https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_method)
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [September 1, 2024, 11:15pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/4 "2024-09-01T23:15:45Z")
> [@khaledharizb](#):
>
> `u[:,i+1] = u[:,i] + h * b[1] * K[1] + h * b[2] * K[2]`
You are adding a vector to a scalar here?
PS. Please don’t post screenshots of text. Post quoted text.
---
### Author:  [@khaledharizb](https://discourse.julialang.org/u/khaledharizb)
#### Post date: [September 1, 2024, 11:32pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/6 "2024-09-01T23:32:10Z")
I solve it but still not working
---
### Author:  [@khaledharizb](https://discourse.julialang.org/u/khaledharizb)
#### Post date: [September 1, 2024, 11:34pm UTC](https://discourse.julialang.org/t/implementation-implicit-gauss-method/118912/7 "2024-09-01T23:34:18Z")
This code is also working but still give me a wrong result
```julia
function RKStep(f,x0,h,A,b)
x=[] ; push!(x,x0);
tol = 1e-12;
for i in 1:N-1;
g(K) = f(x0 + h * A * K);
K = FixIter(g,x0,tol)
x0 = x0 .+ h * b'* K;
push!(x,x0);
end
return stack(x, dims=1)
end
```