An efficient approach for the numerical solution of fifth-order KdV equations

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.

Novel Schemes for Cauchy-Riemann System of Equations with Cauchy Conditions

“…Also, they established the condition for the oscillation of solution. Ahmed et al [2] studied the KdV equations via dierent well known approaches. They have analyzed and noticed the behavior of solution by dierent methods and presented the comparative analysis by computing the error tables.…”

Numerical Solution of the Multiterm Time-Fractional Model for Heat Conductivity by Local Meshless Technique

“…e meshless methods have the ability to compute the solution in regular and irregular domain utilizing scattered or uniform nodes, which increases the priority and the advantages of meshless methods. As these facts show, these methods are really workable and useful numerical methods that can be applied to real-world challenging problems [9][10][11][12][13][14][15][16][17].…”

Hyperbolic Type Solutions for the Couple Boiti-Leon-Pempinelli System

“…There are several approaches for finding solutions of nonlinear partial differential equations which have been developed and employed successfully. Some of these are a new sub equation method [1], homotopy analysis method [2,3], homotopy-Pade method [4], homotopy perturbation method [5,6], (G ′ /G)-expansion method [7,8], modified variational iteration algorithm-I [9,10,11], sub equation method [12], Variational iteration method with an auxiliary parameter [13,14,15,16], sumudu transform approach [17], (1/G ′ )-expansion method [18,19], variational iteration method [20,21], auto-Bäcklund transformation method [22], Clarkson-Kruskal direct method [23], Bernoulli sub-equation function technique [24], decomposition method [25,26,27,28], modified variational iteration algorithm-II [29,30,31], first integral method [32], homogeneous balance method [33], modified Kudryashov technique [34], residual power series approach [35], collocation method [36], extended rational SGEEM [37], sine-Gordon expansion method [38,39] and many more [40,41,...…”