Cyclic Composite Multistep Predictor-Corrector Methods

Block Runge‐Kutta Methods on Parallel Computers

“…CHU and HAMILTON [3] generalized the cyclic linear multistep methods of DONELSON and HANSEN [4]. Families of third-and fourth-order multi-block methods were derived.…”

“…one-stage BRK methods. For example, their second-order method can be represented by the array ~~--- 4) and their fourth-order method by Both methods require only two processors and respectively two and four starting values when implemented in BRK form.…”

Composite exponential approximations

“…In a nutshell, we explore the effect of combining two (or more) different numerical methods with different step-lengths so that the numerical order is increased, while other desirable properties of the solution (stability, exponential fitting, etc.) are retained.In its spirit this work follows two trails: first, the cyclic linear multistep methods [2], [20]. These methods consist of sequential application of several (possibly zero-unstable) linear multistep schemes, each with a constant step-length, so that the outcome, as a whole, is zero-stable and of high order.…”

“…In its spirit this work follows two trails: first, the cyclic linear multistep methods [2], [20]. These methods consist of sequential application of several (possibly zero-unstable) linear multistep schemes, each with a constant step-length, so that the outcome, as a whole, is zero-stable and of high order.…”

Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. I. The nonstiff case

“…The approach developed by Bond can be regarded as a cyclic approach [6], a deferred correction approach [9], a linear multistep method with an off-step point [2], [3], [12], [16] or a block approach [19], [22], [28]. However, a rather more fruitful interpretation is to regard these formulae as explicit Runge-Kutta methods, and the purpose of this paper is to extend Bond's formulae in a Runge-Kutta framework using Butcher's analysis.…”