# MethodError when solving SDE in DifferentialEquations.jl

Hi,

Apologies for not having a more informative title. I’m having a little trouble solving a 2-dimensional SDE in DifferentialEquations.jl. My current code is

``````using DifferentialEquations, ForwardDiff

# Solve Chemical Langevin Equation SDE
# dX = α(X) dt + √β(x) dW

S = [ 1 -1 0; 0 1 -1]

function h(x, c)
return h = [ c[1] * x[1]; c[2] * x[1] * x[2]; c[3] * x[2]]
end

function α(x, c)
return dx = S * h(x, c)
end

function β(x, c)
return σx = S * Diagonal(h(x, c)) * transpose(S)
end

function sqrtβ(x, c)
return sqrt(β(x, c))
end

x0 = [ 70 ; 80 ]

tspan = (0.0, 50.0)

c = [ 1.0, 0.005, 0.6 ]

lotvol_CLE_SDE = SDEProblem(α, sqrtβ, x0, tspan, c)
CLE_sol = solve(lotvol_CLE_SDE)
``````

which, upon running the final line, returns the error

``````> MethodError: no method matching α(::Array{Float64,1}, ::Array{Float64, 1}, ::Float64)
``````

and I can’t totally make sense of this. Is the issue to do with e.g.

• how I’ve written the drift function
• how I’ve passed the drift function to the SDE problem
• how I’ve passed the parameters `c` to the problem

or something else entirely?

Separately, the SDE in question has a multiplicative, non-diagonal noise structure. I’m not sure whether this is causing the problem (the error I’m receiving doesn’t seem to suggest so), but I wanted to get a sanity check on whether I’ve written it sensibly. The examples here were useful, but are phrased in slightly different terms to what I’m used to.

there is no two argument syntax. See the examples in https://diffeq.sciml.ai/stable/tutorials/sde_example/

1 Like

Ah, of course! Thank you. I have changed the functions to

``````function α(dx, x, c, t)
return dx = S * h(x, c)
end

function β(x, c)
return σx = S * Diagonal(h(x, c)) * transpose(S)
end

function sqrtβ(dx, x, c, t)
return sqrt(β(x, c))
end
``````

and the code runs now. I seem to be getting a slightly weird solution for the SDE itself (constant?), but I’ll try to work that out in my own time. Thanks!

`dx .= S * h(x, c)` you’re creating new arrays, but you need to mutate like that.

1 Like

Thanks, I’m getting much more sensible outputs now.