New numerical solutions of fractional-order Korteweg-de Vries equation
Mohammad Partohaghighi, Mehmet Ali Akınlar, Yu‐Ming Chu
Abstract
We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-discretization numerical scheme. Caputo type fractional-order derivative operators are used. We apply the method to some specific cases of the KdV equation. Computational results indicate that the method gives new and highly efficient solutions of the KdV equation.
Topics & Concepts
Korteweg–de Vries equationDiscretizationMathematicsOrder (exchange)Scheme (mathematics)Applied mathematicsFractional calculusType (biology)Mathematical analysisPhysicsNonlinear systemFinanceEconomicsEcologyQuantum mechanicsBiologyFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods for differential equations