Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm

Solution of Nonlinear Stochastic Langevin’s Equation Using WHEP, Pickard and HPM Methods

“…The theorem can be proved using the mathematical induction with the Picard iterative technique as in [7]. The deterministic solution of Equation (2) at 0 ρ = [8], is:…”

“…They have developed a theory of turbulence involving a truncated WHE of the velocity field. This technique was also used by M. El-Tawil and his co-workers [6][7][8][9][10].…”

“…where NC refers to the number of corrections, m is the order, the statistical properties of the solution can be calculated as [7]:…”

“…The WHE method can be used in solving Equation (2). A set of deterministic integro-differential equations are obtained in the deterministic kernels [7],…”

“…A. Georges [4]. The Langevin's equation [5] with square nonlinear losses and stochastic non-homogeneity is solved by using different techniques, mainly the WHEP technique [6][7][8][9][10][11], the Picard approximation [8][9][10] and HPM [9][10][11].…”