Numerical Approximation of Higher-Order Solutions of the Quadratic Nonlinear Stochastic Oscillatory Equation Using WHEP Technique

Abstract

This paper introduces higher-order solutions of the stochastic nonlinear differential equations with the Wiener-Hermite expansion and perturbation (WHEP) technique. The technique is used to study the quadratic nonlinear stochastic oscillatory equation with different orders, different number of corrections, and different strengths of the nonlinear term. The equivalent deterministic equations are derived up to third order and fourth correction. A model numerical integral solver is developed to solve the resulting set of equations. The numerical solver is tested and validated and then used in simulating the stochastic quadratic nonlinear oscillatory motion with different parameters. The solution ensemble average and variance are computed and compared in all cases. The current work extends the use of WHEP technique in solving stochastic nonlinear differential equations.