Polynomial scaling functions for numerical solution of generalized Kuramoto–Sivashinsky equation

Abstract

The current paper proposes a technique for the numerical solution of generalized Kuramoto–Sivashinsky equation. The method is based on finite difference formula combined with the collocation method, which uses the polynomial scaling functions (PSF). Mentioned functions and their properties are employed to derive a general procedure for forming the operational matrix of PSFs. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. An estimation of error bound for this method is presented. Some numerical example is included to demonstrate the validity and applicability of the technique. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use.

Keywords:

• Generalized Kuramoto–Sivashinsky equation
• polynomial scaling functions
• operational matrix of derivative
• error bounds

AMS Subject Classifications:

• 65N06
• 65T60
• 65L60
• 65N15
• 32E30

Notes

No potential conflict of interest was reported by the authors.