# Radial Basis Finite Difference

**URL:** <https://discourse.julialang.org/t/radial-basis-finite-difference/66379>\
**Category:** Performance\
**Created:** [August 14, 2021, 8:24am UTC](https://discourse.julialang.org/t/radial-basis-finite-difference/66379 "2021-08-14T08:24:06Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Manisha\_07](https://avatars.discourse-cdn.com/v4/letter/m/57b2e6/32.png) [@Manisha\_07](https://discourse.julialang.org/u/Manisha_07)\
**Post date:** [August 14, 2021, 8:24am UTC](https://discourse.julialang.org/t/radial-basis-finite-difference/66379/1 "2021-08-14T08:24:06Z")

</div>

Hello People  
I was trying to simulate heat equation using Julia by the method of finite difference.  
I would like to simulate for Radial Basis Finite Difference method also.  
Please help me to find the code for it  
my code for finite difference is

```julia
using Plots
#gr()
L=20
N=100
k=50
x=range(0, stop=100, length=100);
dx=x[2]-x[1];
dt=0.5*dx^2/(2*k);
t=0:dt:10
# print("the vlues of t",t)
#T=zeros(length(t),length(x))
T=zeros(length(x),length(t)) # t <--> x
s=size(T)
print("size of matrix",s)
#T[1,2]=T[1,1]=100 #complete 1st row
#T[end,end]=150 #last row of a matrix
@. T[:, 1] = 100 # initial values
@.T[:,end]=150
#for i in 2:1960
for j in 1:1960 # i -> j
# for j=1:99
    for i=2:99 # j -> i, 1:99 -> 2:99
        T[i,j+1]=T[i,j]+k*dt/(dx^2)*(T[i+1,j]-2*T[i,j] + T[i-1,j])
    end
end
#surface(x,t,T)
surface(t,x,T) # x <--> t

```

---

<div class="post-metadata">

**Author:** ![Christopher\_Fisher](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/christopher_fisher/32/26132_2.png) [@Christopher\_Fisher](https://discourse.julialang.org/u/Christopher_Fisher)\
**Post date:** [August 14, 2021, 9:27am UTC](https://discourse.julialang.org/t/radial-basis-finite-difference/66379/2 "2021-08-14T09:27:26Z")

</div>

This might be useful:

[https://ferrite-fem.github.io/Ferrite.jl/dev/examples/heat\_equation/](https://ferrite-fem.github.io/Ferrite.jl/dev/examples/heat_equation/)

I also found the following in the DifferentialEquations.jl ecosystem:

[https://github.com/SciML/SciMLBenchmarks.jl/blob/df8170422996722331b6cc619f9687f53aa1d3c2/benchmarks/StiffSDE/StochasticHeat.jmd](https://github.com/SciML/SciMLBenchmarks.jl/blob/df8170422996722331b6cc619f9687f53aa1d3c2/benchmarks/StiffSDE/StochasticHeat.jmd)

---

<div class="post-metadata">

**Author:** ![pxshen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pxshen/32/38776_2.png) [@pxshen](https://discourse.julialang.org/u/pxshen)\
**Post date:** [June 22, 2022, 11:21pm UTC](https://discourse.julialang.org/t/radial-basis-finite-difference/66379/3 "2022-06-22T23:21:34Z")

</div>

Check out this `EquivariantOperators.jl` diffusion FDTD [tutorial](https://colab.research.google.com/drive/17JZEdK6aALxvn0JPBJEHGeK2nO1hPnhQ#scrollTo=2xW0gUV_DFXT&line=1&uniqifier=1) and [package website](https://aced-differentiate.github.io/EquivariantOperators.jl/)