Rosenbrock methods with an explicit first stage. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Sandu, Adrian
• Is Part Of: International journal of computer mathematics. Volume 93:Issue 6(2016)
• Page Start: 995
• Page End: 1010
• Publication Date: 2016-06-02
• Subjects: Rosenbrock methods -- order reduction -- parabolic PDEs -- stability analysis -- inexact Jacobians; 65L06; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1012837
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : Traditional Rosenbrock methods suffer from order reduction when applied to partial differential equations with non-homogeneous boundary conditions and source terms. The paper studies a family of Rosenbrock schemes with an explicit first stage. This structure allows one to construct algorithms with high stage orders, and which do not suffer from order reduction. The paper discusses additional order conditions needed for linear stability, for using inexact Jacobians, and implementation aspects. Second- and third-order practical schemes are constructed, and their application to one- and two-dimensional partial differential equations test problems confirm the theoretical findings.