Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODEs) with constant coefficients. Such ODEs arise in the numerical solution of partial differential equations governing linear wave phenomena. The restriction to
Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations
β Scribed by H. Claus
- Publisher
- Springer Vienna
- Year
- 1990
- Tongue
- English
- Weight
- 629 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0010-485X
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We investigate the conditions which guarantee that Runge-Kutta methods preserve asymptotic values of the systems of ordinary differential equations. A complete characterization of such methods is given and examples of methods with these properties are presented for s = p : 2, 3 and 4, where s is the
Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable time-step restrictions when applied to convection-diffusion problems, unless diffusion strongly dominates and an ap