Abstract
Abstract The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations. In order to assess the precision, stability and accuracy of the solutions, five test problems are offered for different types of fifth-order KdV equations. Numerical results are compared with the Adomian decomposition method, Laplace decomposition method, modified Adomian decomposition method and the homotopy perturbation transform method, which reveals that the MVIA-II exceptionally productive, computationally attractive and has more accuracy than the others.
Highlights
Nonlinear partial differential equations (PDEs) have turned into a helpful tool for delineating a large number of physical problems that arise in many fields of mathematics and science, including fluid dynamics, chemical physics, hydrodynamics, fluid mechanics, heat and mass transfer, solid-state physics, chemical kinematics, plasma physics, etc. [1,2,3,4,5,6,7,8,9,10,11,12]
modified variational iteration algorithm-II (MVIA-II) is employed for the numerical treatment of the SK equation, C-D-G equation, a fifth-order Korteweg-de Vries (KdV) equation, Lax equation and Kawahara equation
To show the efficiency and applicability of the proposed algorithm in comparison with adomian decomposition method (ADM) [24] and modified ADM [28], the absolute errors are reported in Tables 1 and 2 for various values of t and x and k = 0.01 and c = 0.0
Summary
Nonlinear partial differential equations (PDEs) have turned into a helpful tool for delineating a large number of physical problems that arise in many fields of mathematics and science, including fluid dynamics, chemical physics, hydrodynamics, fluid mechanics, heat and mass transfer, solid-state physics, chemical kinematics, plasma physics, etc. [1,2,3,4,5,6,7,8,9,10,11,12]. The Korteweg-de Vries (KdV) equation is a nonlinear PDE and assumes a significant role with numerous applications, for example, in illustration of magneto-acoustic waves, ion-acoustic waves, nonlinear LC circuit’s waves and shallow water waves in plasmas.
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