A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations

Mohanty, R. K.; Sharma, Divya

doi:10.1007/s10910-024-01577-w

J Math Chem

2024

DOI: 10.1007/s10910-024-01577-w

|View full text |Cite

A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations

R. K. Mohanty,

Divya Sharma

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations

Sharma,

Mittal,

Kaur

et al. 2024

Numer Algor

View full text Add to dashboard Cite

High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations

Sharma,

Mittal,

Kaur

et al. 2024

Numer Algor

View full text Add to dashboard Cite

A new spline method on graded mesh for fourth-order time-dependent PDEs: application to Kuramoto-Sivashinsky and extended Fisher-Kolmogorov equations

Sharma,

Sharma

2024

Phys. Scr.

View full text Add to dashboard Cite

In this research, we introduce a two-tier non-polynomial spline approach with graded mesh discretization for addressing fourth-order time-dependent partial differential equations, which find applications in various physical scenarios like the nonlinear Kuramoto-Sivashinsky equation and extended Fisher-Kolmogorov equation. Our method involves considering three spatial points at each time step for scheme development, achieving spatial accuracy of three and temporal accuracy of two. Notably, our approach offers the advantage of directly tackling singular biharmonic problems without the need for discretizing boundary conditions or incorporating fictitious points. It demonstrates unconditional stability when tested on fourth-order problems and outperforms previous methods, as evidenced by comparative analyses. Additionally, we present 2D and 3D plots illustrating numerical solutions for different benchmark scenarios, including the depiction of the chaotic nature of the Kuramoto-Sivashinsky equation under Gaussian initial conditions at various time levels.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations

Cited by 2 publications

References 57 publications

High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations

High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations

A new spline method on graded mesh for fourth-order time-dependent PDEs: application to Kuramoto-Sivashinsky and extended Fisher-Kolmogorov equations

Contact Info

Product

Resources

About