Numerical solution of coupled Schrödinger–KdV equation via modified variational iteration algorithm-II

Solving the coupled Schrödinger -Korteweg- de-Vries system by modified variational iteration method with genetic algorithm

“…One of the important nonlinear PDEs is known as Schrodinger-KdV equations are frequently used to simulate the nonlinear dynamics of one-dimensional Langmuir and ion acoustic waves traveling at ion acoustic speeds. The Schrodinger-KdV equation system has been resolved by several authors using a variety of methods, including the variational iteration method [5], the modified variational iteration method [6], the homotopy perturbation method [7], the optimal homotopy asymptotic method [8], the new iterative method [9], the modified laplace decomposition method [10], the compact finite difference scheme [11], the Runge-Kutta structure-preserving methods [12], the (G /G)-expansion technique [13], the differential transform method [14] etc. The (VIM) is one of the most straightforward and efficient methods for locating approximations of (PDEs), and most authors have used it to produce a range of numerical results.…”

Solving fractional Black–Scholes equation by using Boubaker functions

“…In 1997 a study of the Black–Scholes formula for a European option price has revived the Nobel Prize in economic sciences based on the theory of partial differential equations. The theory and applications of partial derivatives are widely used in modeling of applied science and technology 1‐5 . In these very recent years, modeling and numerical solutions of fractional derivative have also been considered as a strong mathematical tool to study a wide spectrum of real‐life occurrences in science and engineering 6‐9 .…”