Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Scientific Computing with Ordinary Differential Equations
Scientific Computing with Ordinary Differential Equations
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
Some secant approximations for Rosenbrock W-methods
Applied Numerical Mathematics
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Implicit methods are the natural choice for solving stiff systems of ODEs. Rosenbrock methods are a class of linear implicit methods for solving such stiff systems of ODEs. In the Rosenbrock methods the exact Jacobian must be evaluated at every step. These evaluations can make the computations costly. By contrast, W-methods use occasional calculations of the Jacobian matrix. This makes the W-methods popular among the class of linear implicit methods for numerical solution of stiff ODEs. However, the design of high-order W-methods is not easy, because as the order of the W-methods increases, the number of order conditions of the W-methods increases very fast. In this paper, we describe an approach to constructing high-order W-methods.