The WHEP technique has the advantage of decoupling the equivalent deterministic system resulting from WHE technique.
Applying the WHEP technique to the system in (7), the final set of equivalent deterministic equations for NC = 2 will be
The deterministic system in (13) resulting from the WHEP technique can be solved analytically.
In our case and with the other variables fixed, the parameter [lambda] controls the convergence of the numerical algorithms (WHE, WHEP, and MCS).
The numerical WHEP and numerical WHE give approximately the same solution.
The numerical WHEP algorithm consumes 33 seconds to get the solution while the numerical WHE requires 83 seconds to converge with residual of [10.sup.-6].
In Section 2, the WHEP technique is reviewed and the generalized WHEP derivation steps are outlined.
This is the main algorithm of the WHEP algorithm .
The WHEP technique for general nonlinear exponent (n), general order (m), and general number of corrections (NC) follows the following steps .
Apply the previous WHEP algorithm to get the following systems of equations of the quadratic (n = 2) nonlinear oscillatory equation and first-order (m = 1) Gaussian approximation and different number of corrections (NC).
For the quadratic nonlinear oscillatory stochastic equation, the application of the WHEP technique will result in the following set of equations (Tables 1, 2, and 3).
It is worth to note that the WHEP technique used in the current work can be extended to solve stochastic PDEs with white noise in multiple dimensions and of different colors as described in .