At every time step I can approximate the change in $Z$ using the following equation:
$$ dZ = f(Z_{prev}, X_{prev})dt + CdW_t, \quad(1)$$
$$dW_t = r\sqrt{dt}$$
where $C$ is some constant, and $r$ is a normally distributed value. Based on this I will have a guess for $Z_{next}$: $$ Z_{next} = Z_{prev} + dZ$$
I ask because I am interested in writing a simple MATLAB solver for this type of an SDE, based on the algorithm I outlined above. However, I am not sure if the algorithm makes sense, and I am having trouble searching for resources to answer this question because I am not sure what to call an SDE of the form presented in equation $(1)$.
Most SDE solution schemes e.g. Euler-Mauryama assume an SDE of the form:
$$ dZ = f(Z_{prev})dt + gZ_{prev}dW_t$$
but my $dW_t$ term does not depend on $Z_{prev}$.