Asset Details
Do you wish to reserve the book?
A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs
Do you wish to request the book?
A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs
2025
Overview
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered in this paper. Despite superior efficiency due to the compact stencils, the scheme’s stability analysis is much harder for the cumbersome expression of amplification matrix. We present a theoretical investigation of spectral radius using matrix method, as the popular von Neumann stability analysis is not applicable to the schemes for variable coefficient PDEs. Thereby a sufficient condition for the stability of the compact scheme is derived using a difference equation based approach. Subsequently, the constant coefficient PDEs are considered as a special case, and the unconditional stability of the schemes for such case is proved theoretically. An estimate of condition number of the amplification matrix is derived to study the robustness of the scheme. As an application, the Black–Scholes PDE for option pricing is numerically solved in both variable and constant coefficient frameworks. The numerical illustrations evidently support the theoretical findings.
Publisher
Springer Nature B.V
