Constructions of solitary travelling wave solutions for Ito integro-differential equation arising in plasma physics

Abstract

Constructing exact and numerical solutions of partial differential equations (PDEs) has become an active area in recent years. This work focuses on developing new exact and numerical solutions for (1+1)- dimensional Ito integro-differential equation by applying exp(-f(ζ))-expansion and finite difference methods, respectively. Trigonometric, hyperbolic and rational solutions are successfully presented. The stability and accuracy of the obtained numerical simulation are discussed. The presented graphical comparison shows that the exact and numerical solutions nearly coincide with each other. L2 error which illustrates the effectiveness of the used numerical approach is comprehensively studied. The applied methods can be effectively invoked to solve more nonlinear PDEs.