Numerical treatment of multi-term time fractional nonlinear KdV equations with weakly singular solutions

ABSTRACT

The main aim of this work is to construct an efficient recursive numerical technique for solving multi-term time fractional nonlinear KdV equation. The fractional derivatives are defined in Caputo sense. A modified Laplace decomposition method is introduced to approximate the solution. The Adomian polynomials play an important role to execute such a recursive process. In addition, the mathematical importance and some applications of KdV equation are discussed. The approximate solution obtained by the proposed method can be expressed in the form of an infinite convergent series. The experimental evidences demonstrate the effectiveness of the proposed method.

KEYWORDS:

• Fractional Kdv equation
• Caputo derivative
• Adomain decomposition method
• Laplace transform
• convergence analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Sudarshan Santra

Mr. Sudarshan Santra, is a research scholar in the Dept. of Mathematics, National Institute of Technology Rourkela, India. His research area is Numerical Analysis including numerical solutions for fractional integro-differential equations.

Jugal Mohapatra

Dr. Jugal Mohapatra, currently working as an Associate Professor in the Dept. of Mathematics, National Institute of Technology Rourkela, India. His research area is Numerical Analysis including numerical solutions for fractional integro-differential equations and singularly perturbed differential equations.