Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to generate a smooth curve by connecting at given data points. In this work, an application of fifth degree basis spline functions is presented for a numerica...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 21
Main Authors: Iqbal, Muhammad Kashif, Abbas, Muhammad, Nazir, Tahir, Ali, Nouman
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.10.2020
SpringerOpen
Subjects:
Analysis
Applications
Crank–Nicolson scheme
Difference and Functional Equations
Functional Analysis
Kuramoto–Sivashinsky equation
Mathematics
Mathematics and Statistics
Methods
Ordinary Differential Equations
Partial Differential Equations
Quintic polynomial B-spline functions
Spline approximations
Topics in Special Functions and q-Special Functions: Theory
Von Neumann stability analysis
Von Neumann stability analysis
Quintic polynomial B-spline functions
Spline approximations
Kuramoto–Sivashinsky equation
Crank–Nicolson scheme
ISSN:1687-1847, 1687-1847
Online Access:Get full text
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Summary:A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to generate a smooth curve by connecting at given data points. In this work, an application of fifth degree basis spline functions is presented for a numerical investigation of the Kuramoto–Sivashinsky equation. The finite forward difference formula is used for temporal integration, whereas the basis splines, together with a new approximation for fourth order spatial derivative, are brought into play for discretization in space direction. In order to corroborate the presented numerical algorithm, some test problems are considered and the computational results are compared with existing methods.
ISSN:1687-1847
1687-1847
DOI:10.1186/s13662-020-03007-y