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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Vydáno v:	Advances in difference equations Ročník 2020; číslo 1; s. 1 - 21
Hlavní autoři:	Iqbal, Muhammad Kashif, Abbas, Muhammad, Nazir, Tahir, Ali, Nouman
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 07.10.2020 SpringerOpen
Témata:	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
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Abstract	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.
AbstractList	Abstract 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. 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.
ArticleNumber	558
Author	Iqbal, Muhammad Kashif Nazir, Tahir Ali, Nouman Abbas, Muhammad
Author_xml	– sequence: 1 givenname: Muhammad Kashif orcidid: 0000-0003-4442-7498 surname: Iqbal fullname: Iqbal, Muhammad Kashif email: kashifiqbal@gcuf.edu.pk organization: Department of Mathematics, Government College University – sequence: 2 givenname: Muhammad orcidid: 0000-0002-0491-1528 surname: Abbas fullname: Abbas, Muhammad organization: Department of Mathematics, University of Sargodha – sequence: 3 givenname: Tahir surname: Nazir fullname: Nazir, Tahir organization: Department of Mathematics, University of Sargodha – sequence: 4 givenname: Nouman surname: Ali fullname: Ali, Nouman organization: Department of Software Engineering, Mirpur University of Science & Technology
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Keywords	Von Neumann stability analysis Quintic polynomial B-spline functions Spline approximations Kuramoto–Sivashinsky equation Crank–Nicolson scheme
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Snippet	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... Abstract A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to...
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SubjectTerms	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
Title	Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation
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