  In this article, we present an orthogonal basis expansion method for solving
stochastic differential equations with a path-independent solution of the form
$X_{t}=\phi(t,W_{t})$. For this purpose, we define a Hilbert space and
construct an orthogonal basis for this inner product space with the aid of
2D-Hermite polynomials. With considering $X_{t}$ as orthogonal basis expansion,
this method is implemented and the expansion coefficients are obtained by
solving a system of nonlinear integro-differential equations. The strength of
such a method is that expectation and variance of the solution is computed by
these coefficients directly. Eventually, numerical results demonstrate its
validity and efficiency in comparison with other numerical methods.
