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Runge–Kutta methods for linear ordinary differential equations (1999)
| Content Provider | CiteSeerX |
|---|---|
| Author | Zingg, David W. Chisholm, Todd T. Zingg, D. W. Chisholm, T. T. |
| Abstract | 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 the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations. |
| File Format | |
| Volume Number | 31 |
| Journal | Appl. Numer. Math |
| Language | English |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Runge Kutta Method Linear Ordinary Differential Equation Constant Coefficient Dependent Variable Fourth-order Method Numerical Solution High-order Spatial Discretizations Excellent Option Numerical Integration Conventional Runge-kutta Method Runge-kutta Method Linear Inhomogeneous Ordinary Differential Equation Memory Location Excellent Choice Conventional Counterpart Sixth-order Method Partial Differential Equation Classical Fourth-order Runge-kutta Method Ode Arise Primary Concern Linear Wave Phenomenon New Runge-kutta Method |
| Content Type | Text |
| Resource Type | Article |
