Unconventional Schemes for a Class of Ordinary Differential Equations—With Applications to the Korteweg–de Vries Equation

✍ Scribed by William Kahan; Ren-Chang Li

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 600 KB
• Volume: 134
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5710

✦ Synopsis

But we shall study it elsewhere.

An unconventional numerical method for solving a restrictive and yet often-encountered class of ordinary differential equations is In general a system of ordinary differential equations proposed. The method has a crucial, what we call reflexive, property for which f(y) is a polynomial in y, can be transformed and requires solving one linear system per time-step, but is secondinto a big system like (1.1) and (1.2) by introducing a new order accurate. A systematical and easily implementable scheme is variables. Unfortunately doing so may end up with an proposed to enhance the computational efficiency of such methods unstable system, even though the original system is stable.

whenever needed. Applications are reported on how the idea can be applied to solve the Korteweg-de Vries Equation discretized in

In this paper, we propose efficient numerical methods space. ᮊ 1997 Academic Press for solving such a system. Special attention will be given to how the idea can be applied to solve the discretized Korteweg-de Vries (KdV) equations.