Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

Abstract

In this paper, one of the nonlinear evolution equation (NLEE) namely generalised Oskolkov equation which defines the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid is investigated. We discuss numerical
 solutions of the equation for two test problems including single solitary wave and Gaussian initial condition, applying the collocation finite element method. The algorithm, based upon Crank Nicolson approach in time, is unconditionally stable. To demonstrate the proficiency and accuracy of the numerical algorithm, error norms L2, L∞ and invariant I are calculated and the obtained results are indicated both in tabular and graphical form. The obtained numerical results provide the method is more suitable and systematically handle the solution procedures of nonlinear equations arising in mathematical physics.