Explicit multi-step peer methods for special second-order differential equations
The paper is concerned with the solution of non-stiff second order initial value problems where the right hand side has no dependence upon \(y'\). The methods under consideration are explicit two- and three-step peer methods of order \(p=2s\). The paper is structured as follows: The authors describe how the numerical methods are formulated, then consider the theory of multi-step peer methods including convergence and stability. This enables the construction of methods having optimal zero stability. Implementational issues are considered and finally numerical results are given that show how the methods perform for a variety of test problems. Comparisons with existing alternative methods show the peer methods to be competitive. Parallel and sequential methods are discussed.
scientific article; zbMATH DE number 5321672
scientific article