An efficient approach for the numerical solution of fifth-order KdV equations
Hijaz Ahmad, Tufail A. Khan, Shao-Wen Yao
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.
Topics & Concepts
Adomian decomposition methodKorteweg–de Vries equationMathematicsLaplace transformPerturbation (astronomy)Applied mathematicsHomotopyDecompositionHomotopy perturbation methodDecomposition method (queueing theory)Mathematical analysisPartial differential equationNonlinear systemPure mathematicsDiscrete mathematicsBiologyQuantum mechanicsEcologyPhysicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsAlgebraic structures and combinatorial models