Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs

• Published in: Journal of computational and applied mathematics Vol. 303; pp. 218 - 228
• Main Author: Abdi, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2016
• Subjects: [formula omitted]- and [formula omitted]- stability; Computation; Constants; Construction; Derivatives; Differential equations; Errors; General linear methods; Mathematical models; Numerical integration; Quadratic stability; Second derivative methods; Stiff differential equations; Stiff differential equations; General linear methods; A- and L- stability; Second derivative methods; Quadratic stability
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2016.02.054

Theory of general linear methods (GLMs) for the numerical solution of autonomous system of ordinary differential equations of the form y′=f(y) is extended to include the second derivative y″=g(y):=f′(y)f(y). This extension of GLMs is called second derivative general linear methods (SGLMs). In this paper we will construct two-stage A- and L-stable SGLMs of order p and stage order q=p up to six with low error constants. We will show the efficiency of the proposed methods by implementing on some well-known stiff problems.